spherical, log-radial, coordinate
chart coordinates: $x^\tilde{\mu} = \{\rho, \theta, \phi\}$
chart coordinate basis: $e_\tilde{\mu} = \{e_{\tilde{\rho}}, e_{\tilde{\theta}}, e_{\tilde{\phi}}\}$
embedding coordinates: $u^I = \{x, y, z\}$
embedding basis $e_I = \{e_{x}, e_{y}, e_{z}\}$
transform from basis to coordinate:
${{{ \tilde{e}}_{\rho}}^{\rho}} = {1}$;
${{{ \tilde{e}}_{\theta}}^{\theta}} = {1}$;
${{{ \tilde{e}}_{\phi}}^{\phi}} = {1}$
transform from coorinate to basis:
${{{ \tilde{e}}^{\rho}}_{\rho}} = {1}$;
${{{ \tilde{e}}^{\theta}}_{\theta}} = {1}$;
${{{ \tilde{e}}^{\phi}}_{\phi}} = {1}$
tensor index associated with coordinate $\rho$ is index $\rho$ with operator $e_{\rho}(\zeta) = $$\frac{\partial \zeta}{\partial \rho}$
tensor index associated with coordinate $\theta$ is index $\theta$ with operator $e_{\theta}(\zeta) = $$\frac{\partial \zeta}{\partial \theta}$
tensor index associated with coordinate $\phi$ is index $\phi$ with operator $e_{\phi}(\zeta) = $$\frac{\partial \zeta}{\partial \phi}$
flat metric:
${{{ \eta}_x}_x} = {1}$;
${{{ \eta}_y}_y} = {1}$;
${{{ \eta}_z}_z} = {1}$
chart in embedded coordinates:
${{ u}^x} = {{{\frac{{{A}} {{sinh\left( {{\frac{1}{w}}{({\rho})}}\right)}}}{sinh\left( {\frac{1}{w}}\right)}}} {{sin\left( \theta\right)}} {{cos\left( \phi\right)}}}$;
${{ u}^y} = {{{\frac{{{A}} {{sinh\left( {{\frac{1}{w}}{({\rho})}}\right)}}}{sinh\left( {\frac{1}{w}}\right)}}} {{sin\left( \theta\right)}} {{sin\left( \phi\right)}}}$;
${{ u}^z} = {{{\frac{{{A}} {{sinh\left( {{\frac{1}{w}}{({\rho})}}\right)}}}{sinh\left( {\frac{1}{w}}\right)}}} {{cos\left( \theta\right)}}}$
basis operators applied to chart:
${{{ e}_u}^I} = {{{ u}^I}_{,u}}$
${{{ e}_{\rho}}^x} = {\frac{{{A}} {{cosh\left( {{\frac{1}{w}}{({\rho})}}\right)}} {{sin\left( \theta\right)}} {{cos\left( \phi\right)}}}{{{w}} {{sinh\left( {\frac{1}{w}}\right)}}}}$;
${{{ e}_{\rho}}^y} = {\frac{{{A}} {{cosh\left( {{\frac{1}{w}}{({\rho})}}\right)}} {{sin\left( \theta\right)}} {{sin\left( \phi\right)}}}{{{w}} {{sinh\left( {\frac{1}{w}}\right)}}}}$;
${{{ e}_{\rho}}^z} = {\frac{{{A}} {{cosh\left( {{\frac{1}{w}}{({\rho})}}\right)}} {{cos\left( \theta\right)}}}{{{w}} {{sinh\left( {\frac{1}{w}}\right)}}}}$;
${{{ e}_{\theta}}^x} = {\frac{{{A}} {{cos\left( \theta\right)}} {{sinh\left( {{\frac{1}{w}}{({\rho})}}\right)}} {{cos\left( \phi\right)}}}{sinh\left( {\frac{1}{w}}\right)}}$;
${{{ e}_{\theta}}^y} = {\frac{{{A}} {{cos\left( \theta\right)}} {{sinh\left( {{\frac{1}{w}}{({\rho})}}\right)}} {{sin\left( \phi\right)}}}{sinh\left( {\frac{1}{w}}\right)}}$;
${{{ e}_{\theta}}^z} = {\frac{-{{{A}} {{sinh\left( {{\frac{1}{w}}{({\rho})}}\right)}} {{sin\left( \theta\right)}}}}{sinh\left( {\frac{1}{w}}\right)}}$;
${{{ e}_{\phi}}^x} = {\frac{-{{{A}} {{sin\left( \phi\right)}} {{sin\left( \theta\right)}} {{sinh\left( {{\frac{1}{w}}{({\rho})}}\right)}}}}{sinh\left( {\frac{1}{w}}\right)}}$;
${{{ e}_{\phi}}^y} = {\frac{{{A}} {{sin\left( \theta\right)}} {{sinh\left( {{\frac{1}{w}}{({\rho})}}\right)}} {{cos\left( \phi\right)}}}{sinh\left( {\frac{1}{w}}\right)}}$
${{{ e}^{\rho}}_x} = {\frac{{{w}} {{sin\left( \theta\right)}} {{cos\left( \phi\right)}} {{sinh\left( {\frac{1}{w}}\right)}}}{{{A}} {{cosh\left( {{\frac{1}{w}}{({\rho})}}\right)}}}}$;
${{{ e}^{\rho}}_y} = {\frac{{{w}} {{sin\left( \theta\right)}} {{sin\left( \phi\right)}} {{sinh\left( {\frac{1}{w}}\right)}}}{{{A}} {{cosh\left( {{\frac{1}{w}}{({\rho})}}\right)}}}}$;
${{{ e}^{\rho}}_z} = {\frac{{{w}} {{cos\left( \theta\right)}} {{sinh\left( {\frac{1}{w}}\right)}}}{{{A}} {{cosh\left( {{\frac{1}{w}}{({\rho})}}\right)}}}}$;
${{{ e}^{\theta}}_x} = {\frac{{{cos\left( \theta\right)}} {{cos\left( \phi\right)}} {{sinh\left( {\frac{1}{w}}\right)}}}{{{A}} {{sinh\left( {{\frac{1}{w}}{({\rho})}}\right)}}}}$;
${{{ e}^{\theta}}_y} = {\frac{{{sinh\left( {\frac{1}{w}}\right)}} {{cos\left( \theta\right)}} {{sin\left( \phi\right)}}}{{{A}} {{sinh\left( {{\frac{1}{w}}{({\rho})}}\right)}}}}$;
${{{ e}^{\theta}}_z} = {\frac{-{{{sinh\left( {\frac{1}{w}}\right)}} {{sin\left( \theta\right)}}}}{{{A}} {{sinh\left( {{\frac{1}{w}}{({\rho})}}\right)}}}}$;
${{{ e}^{\phi}}_x} = {\frac{-{{{sin\left( \phi\right)}} {{sinh\left( {\frac{1}{w}}\right)}}}}{{{A}} {{sinh\left( {{\frac{1}{w}}{({\rho})}}\right)}} {{sin\left( \theta\right)}}}}$;
${{{ e}^{\phi}}_y} = {\frac{{{sinh\left( {\frac{1}{w}}\right)}} {{cos\left( \phi\right)}}}{{{A}} {{sinh\left( {{\frac{1}{w}}{({\rho})}}\right)}} {{sin\left( \theta\right)}}}}$
${{{{{ e}_u}^I}} {{{{ e}^v}_I}}} = {\overset{u\downarrow v\rightarrow}{\left[\begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix}\right]}}$
${{{{{ e}_u}^I}} {{{{ e}^u}_J}}} = {\overset{I\downarrow J\rightarrow}{\left[\begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix}\right]}}$
basis determinant: ${det(e)} = {\frac{{{{A}^{3}}} {{{sinh\left( {{\frac{1}{w}}{({\rho})}}\right)}^{2}}} {{cosh\left( {{\frac{1}{w}}{({\rho})}}\right)}} {{sin\left( \theta\right)}}}{{{w}} {{{sinh\left( {\frac{1}{w}}\right)}^{3}}}}}$
${{{{ c}_a}_b}^c} = {0}$
${{{ g}_u}_v} = {{{{{ e}_u}^I}} {{{{ e}_v}^J}} {{{{ \eta}_I}_J}}}$
${{{ g}_{\rho}}_{\rho}} = {\frac{{{{A}^{2}}} {{{cosh\left( {{\frac{1}{w}}{({\rho})}}\right)}^{2}}}}{{{{w}^{2}}} {{{sinh\left( {\frac{1}{w}}\right)}^{2}}}}}$;
${{{ g}_{\theta}}_{\theta}} = {\frac{{{{A}^{2}}} {{{sinh\left( {{\frac{1}{w}}{({\rho})}}\right)}^{2}}}}{{sinh\left( {\frac{1}{w}}\right)}^{2}}}$;
${{{ g}_{\phi}}_{\phi}} = {\frac{-{{{{A}^{2}}} {{{sinh\left( {{\frac{1}{w}}{({\rho})}}\right)}^{2}}} {{({{-{1}} + {{cos\left( \theta\right)}^{2}}})}}}}{{sinh\left( {\frac{1}{w}}\right)}^{2}}}$
${{{ g}_u}_v} = {{{{{ e}_u}^I}} {{{{ e}_v}^J}} {{{{ \eta}_I}_J}}}$
metric determinant: ${det(g)} = {\frac{-{{{{A}^{6}}} {{{cosh\left( {{\frac{1}{w}}{({\rho})}}\right)}^{2}}} {{{sinh\left( {{\frac{1}{w}}{({\rho})}}\right)}^{4}}} {{({{-{1}} + {{cos\left( \theta\right)}^{2}}})}}}}{{{{w}^{2}}} {{{sinh\left( {\frac{1}{w}}\right)}^{6}}}}}$
${{{{ \Gamma}_a}_b}_c} = {{{\frac{1}{2}}} {{({{{{{{{{ g}_a}_b}_{,c}} + {{{{ g}_a}_c}_{,b}}} - {{{{ g}_b}_c}_{,a}}} + {{{{ c}_a}_b}_c} + {{{{ c}_a}_c}_b}} - {{{{ c}_c}_b}_a}})}}}$
commutation coefficients:
${{{{ c}_a}_b}^c} = {0}$
metric:
${{{ g}_{\rho}}_{\rho}} = {\frac{{{{A}^{2}}} {{{cosh\left( {{\frac{1}{w}}{({\rho})}}\right)}^{2}}}}{{{{w}^{2}}} {{{sinh\left( {\frac{1}{w}}\right)}^{2}}}}}$;
${{{ g}_{\theta}}_{\theta}} = {\frac{{{{A}^{2}}} {{{sinh\left( {{\frac{1}{w}}{({\rho})}}\right)}^{2}}}}{{sinh\left( {\frac{1}{w}}\right)}^{2}}}$;
${{{ g}_{\phi}}_{\phi}} = {\frac{-{{{{A}^{2}}} {{{sinh\left( {{\frac{1}{w}}{({\rho})}}\right)}^{2}}} {{({{-{1}} + {{cos\left( \theta\right)}^{2}}})}}}}{{sinh\left( {\frac{1}{w}}\right)}^{2}}}$
metric inverse:
${{{ g}^{\rho}}^{\rho}} = {\frac{{{{w}^{2}}} {{{sinh\left( {\frac{1}{w}}\right)}^{2}}}}{{{{A}^{2}}} {{{cosh\left( {{\frac{1}{w}}{({\rho})}}\right)}^{2}}}}}$;
${{{ g}^{\theta}}^{\theta}} = {\frac{{sinh\left( {\frac{1}{w}}\right)}^{2}}{{{{A}^{2}}} {{{sinh\left( {{\frac{1}{w}}{({\rho})}}\right)}^{2}}}}}$;
${{{ g}^{\phi}}^{\phi}} = {\frac{{sinh\left( {\frac{1}{w}}\right)}^{2}}{-{{{{A}^{2}}} {{{sinh\left( {{\frac{1}{w}}{({\rho})}}\right)}^{2}}} {{({{-{1}} + {{cos\left( \theta\right)}^{2}}})}}}}}$
metric derivative:
${{{{ {\partial g}}_{\rho}}_{\rho}}_{\rho}} = {\frac{{{2}} {{{A}^{2}}} {{cosh\left( {{\frac{1}{w}}{({\rho})}}\right)}} {{sinh\left( {{\frac{1}{w}}{({\rho})}}\right)}}}{{{{w}^{3}}} {{{sinh\left( {\frac{1}{w}}\right)}^{2}}}}}$;
${{{{ {\partial g}}_{\theta}}_{\theta}}_{\rho}} = {\frac{{{2}} {{{A}^{2}}} {{cosh\left( {{\frac{1}{w}}{({\rho})}}\right)}} {{sinh\left( {{\frac{1}{w}}{({\rho})}}\right)}}}{{{w}} {{{sinh\left( {\frac{1}{w}}\right)}^{2}}}}}$;
${{{{ {\partial g}}_{\phi}}_{\phi}}_{\rho}} = {\frac{-{{{2}} {{{A}^{2}}} {{sinh\left( {{\frac{1}{w}}{({\rho})}}\right)}} {{cosh\left( {{\frac{1}{w}}{({\rho})}}\right)}} {{({{-{1}} + {{cos\left( \theta\right)}^{2}}})}}}}{{{w}} {{{sinh\left( {\frac{1}{w}}\right)}^{2}}}}}$;
${{{{ {\partial g}}_{\phi}}_{\phi}}_{\theta}} = {\frac{{{2}} {{{A}^{2}}} {{{sinh\left( {{\frac{1}{w}}{({\rho})}}\right)}^{2}}} {{sin\left( \theta\right)}} {{cos\left( \theta\right)}}}{{sinh\left( {\frac{1}{w}}\right)}^{2}}}$
1st kind Christoffel:
${{{{ \Gamma}_{\rho}}_{\rho}}_{\rho}} = {\frac{{{{A}^{2}}} {{cosh\left( {{\frac{1}{w}}{({\rho})}}\right)}} {{sinh\left( {{\frac{1}{w}}{({\rho})}}\right)}}}{{{{w}^{3}}} {{{sinh\left( {\frac{1}{w}}\right)}^{2}}}}}$;
${{{{ \Gamma}_{\rho}}_{\theta}}_{\theta}} = {\frac{-{{{{A}^{2}}} {{sinh\left( {{\frac{1}{w}}{({\rho})}}\right)}} {{cosh\left( {{\frac{1}{w}}{({\rho})}}\right)}}}}{{{w}} {{{sinh\left( {\frac{1}{w}}\right)}^{2}}}}}$;
${{{{ \Gamma}_{\rho}}_{\phi}}_{\phi}} = {\frac{{{{A}^{2}}} {{sinh\left( {{\frac{1}{w}}{({\rho})}}\right)}} {{cosh\left( {{\frac{1}{w}}{({\rho})}}\right)}} {{({{-{1}} + {{cos\left( \theta\right)}^{2}}})}}}{{{w}} {{{sinh\left( {\frac{1}{w}}\right)}^{2}}}}}$;
${{{{ \Gamma}_{\theta}}_{\rho}}_{\theta}} = {\frac{{{{A}^{2}}} {{cosh\left( {{\frac{1}{w}}{({\rho})}}\right)}} {{sinh\left( {{\frac{1}{w}}{({\rho})}}\right)}}}{{{w}} {{{sinh\left( {\frac{1}{w}}\right)}^{2}}}}}$;
${{{{ \Gamma}_{\theta}}_{\theta}}_{\rho}} = {\frac{{{{A}^{2}}} {{cosh\left( {{\frac{1}{w}}{({\rho})}}\right)}} {{sinh\left( {{\frac{1}{w}}{({\rho})}}\right)}}}{{{w}} {{{sinh\left( {\frac{1}{w}}\right)}^{2}}}}}$;
${{{{ \Gamma}_{\theta}}_{\phi}}_{\phi}} = {\frac{-{{{{A}^{2}}} {{{sinh\left( {{\frac{1}{w}}{({\rho})}}\right)}^{2}}} {{sin\left( \theta\right)}} {{cos\left( \theta\right)}}}}{{sinh\left( {\frac{1}{w}}\right)}^{2}}}$;
${{{{ \Gamma}_{\phi}}_{\rho}}_{\phi}} = {\frac{-{{{{A}^{2}}} {{cosh\left( {{\frac{1}{w}}{({\rho})}}\right)}} {{sinh\left( {{\frac{1}{w}}{({\rho})}}\right)}} {{({{-{1}} + {{cos\left( \theta\right)}^{2}}})}}}}{{{w}} {{{sinh\left( {\frac{1}{w}}\right)}^{2}}}}}$;
${{{{ \Gamma}_{\phi}}_{\theta}}_{\phi}} = {\frac{{{{A}^{2}}} {{{sinh\left( {{\frac{1}{w}}{({\rho})}}\right)}^{2}}} {{sin\left( \theta\right)}} {{cos\left( \theta\right)}}}{{sinh\left( {\frac{1}{w}}\right)}^{2}}}$;
${{{{ \Gamma}_{\phi}}_{\phi}}_{\rho}} = {\frac{-{{{{A}^{2}}} {{cosh\left( {{\frac{1}{w}}{({\rho})}}\right)}} {{sinh\left( {{\frac{1}{w}}{({\rho})}}\right)}} {{({{-{1}} + {{cos\left( \theta\right)}^{2}}})}}}}{{{w}} {{{sinh\left( {\frac{1}{w}}\right)}^{2}}}}}$;
${{{{ \Gamma}_{\phi}}_{\phi}}_{\theta}} = {\frac{{{{A}^{2}}} {{{sinh\left( {{\frac{1}{w}}{({\rho})}}\right)}^{2}}} {{sin\left( \theta\right)}} {{cos\left( \theta\right)}}}{{sinh\left( {\frac{1}{w}}\right)}^{2}}}$
connection coefficients / 2nd kind Christoffel:
${{{{ \Gamma}^{\rho}}_{\rho}}_{\rho}} = {\frac{sinh\left( {{\frac{1}{w}}{({\rho})}}\right)}{{{w}} {{cosh\left( {{\frac{1}{w}}{({\rho})}}\right)}}}}$;
${{{{ \Gamma}^{\rho}}_{\theta}}_{\theta}} = {\frac{-{{{w}} {{sinh\left( {{\frac{1}{w}}{({\rho})}}\right)}}}}{cosh\left( {{\frac{1}{w}}{({\rho})}}\right)}}$;
${{{{ \Gamma}^{\rho}}_{\phi}}_{\phi}} = {\frac{{{w}} {{sinh\left( {{\frac{1}{w}}{({\rho})}}\right)}} {{({{-{1}} + {{cos\left( \theta\right)}^{2}}})}}}{cosh\left( {{\frac{1}{w}}{({\rho})}}\right)}}$;
${{{{ \Gamma}^{\theta}}_{\rho}}_{\theta}} = {\frac{cosh\left( {{\frac{1}{w}}{({\rho})}}\right)}{{{w}} {{sinh\left( {{\frac{1}{w}}{({\rho})}}\right)}}}}$;
${{{{ \Gamma}^{\theta}}_{\theta}}_{\rho}} = {\frac{cosh\left( {{\frac{1}{w}}{({\rho})}}\right)}{{{w}} {{sinh\left( {{\frac{1}{w}}{({\rho})}}\right)}}}}$;
${{{{ \Gamma}^{\theta}}_{\phi}}_{\phi}} = {-{{{sin\left( \theta\right)}} {{cos\left( \theta\right)}}}}$;
${{{{ \Gamma}^{\phi}}_{\rho}}_{\phi}} = {\frac{cosh\left( {{\frac{1}{w}}{({\rho})}}\right)}{{{w}} {{sinh\left( {{\frac{1}{w}}{({\rho})}}\right)}}}}$;
${{{{ \Gamma}^{\phi}}_{\theta}}_{\phi}} = {\frac{cos\left( \theta\right)}{sin\left( \theta\right)}}$;
${{{{ \Gamma}^{\phi}}_{\phi}}_{\rho}} = {\frac{cosh\left( {{\frac{1}{w}}{({\rho})}}\right)}{{{w}} {{sinh\left( {{\frac{1}{w}}{({\rho})}}\right)}}}}$;
${{{{ \Gamma}^{\phi}}_{\phi}}_{\theta}} = {\frac{cos\left( \theta\right)}{sin\left( \theta\right)}}$
connection coefficients derivative:
${{{{{ {\partial \Gamma}}^{\rho}}_{\rho}}_{\rho}}_{\rho}} = {\frac{{{({{cosh\left( {{\frac{1}{w}}{({\rho})}}\right)} - {sinh\left( {{\frac{1}{w}}{({\rho})}}\right)}})}} {{({{cosh\left( {{\frac{1}{w}}{({\rho})}}\right)} + {sinh\left( {{\frac{1}{w}}{({\rho})}}\right)}})}}}{{{{w}^{2}}} {{{cosh\left( {{\frac{1}{w}}{({\rho})}}\right)}^{2}}}}}$;
${{{{{ {\partial \Gamma}}^{\rho}}_{\theta}}_{\theta}}_{\rho}} = {\frac{-{({{{cosh\left( {{\frac{1}{w}}{({\rho})}}\right)}^{2}} - {{sinh\left( {{\frac{1}{w}}{({\rho})}}\right)}^{2}}})}}{{cosh\left( {{\frac{1}{w}}{({\rho})}}\right)}^{2}}}$;
${{{{{ {\partial \Gamma}}^{\rho}}_{\phi}}_{\phi}}_{\rho}} = {\frac{{-{{cosh\left( {{\frac{1}{w}}{({\rho})}}\right)}^{2}}} + {{sinh\left( {{\frac{1}{w}}{({\rho})}}\right)}^{2}} + {{{{{cosh\left( {{\frac{1}{w}}{({\rho})}}\right)}^{2}}} {{{cos\left( \theta\right)}^{2}}}} - {{{{cos\left( \theta\right)}^{2}}} {{{sinh\left( {{\frac{1}{w}}{({\rho})}}\right)}^{2}}}}}}{{cosh\left( {{\frac{1}{w}}{({\rho})}}\right)}^{2}}}$;
${{{{{ {\partial \Gamma}}^{\rho}}_{\phi}}_{\phi}}_{\theta}} = {\frac{-{{{2}} {{w}} {{cos\left( \theta\right)}} {{sin\left( \theta\right)}} {{sinh\left( {{\frac{1}{w}}{({\rho})}}\right)}}}}{cosh\left( {{\frac{1}{w}}{({\rho})}}\right)}}$;
${{{{{ {\partial \Gamma}}^{\theta}}_{\rho}}_{\theta}}_{\rho}} = {\frac{{{({{sinh\left( {{\frac{1}{w}}{({\rho})}}\right)} - {cosh\left( {{\frac{1}{w}}{({\rho})}}\right)}})}} {{({{sinh\left( {{\frac{1}{w}}{({\rho})}}\right)} + {cosh\left( {{\frac{1}{w}}{({\rho})}}\right)}})}}}{{{{w}^{2}}} {{{sinh\left( {{\frac{1}{w}}{({\rho})}}\right)}^{2}}}}}$;
${{{{{ {\partial \Gamma}}^{\theta}}_{\theta}}_{\rho}}_{\rho}} = {\frac{{{({{sinh\left( {{\frac{1}{w}}{({\rho})}}\right)} - {cosh\left( {{\frac{1}{w}}{({\rho})}}\right)}})}} {{({{sinh\left( {{\frac{1}{w}}{({\rho})}}\right)} + {cosh\left( {{\frac{1}{w}}{({\rho})}}\right)}})}}}{{{{w}^{2}}} {{{sinh\left( {{\frac{1}{w}}{({\rho})}}\right)}^{2}}}}}$;
${{{{{ {\partial \Gamma}}^{\theta}}_{\phi}}_{\phi}}_{\theta}} = {{{({{sin\left( \theta\right)} - {cos\left( \theta\right)}})}} {{({{sin\left( \theta\right)} + {cos\left( \theta\right)}})}}}$;
${{{{{ {\partial \Gamma}}^{\phi}}_{\rho}}_{\phi}}_{\rho}} = {\frac{{{({{sinh\left( {{\frac{1}{w}}{({\rho})}}\right)} - {cosh\left( {{\frac{1}{w}}{({\rho})}}\right)}})}} {{({{sinh\left( {{\frac{1}{w}}{({\rho})}}\right)} + {cosh\left( {{\frac{1}{w}}{({\rho})}}\right)}})}}}{{{{w}^{2}}} {{{sinh\left( {{\frac{1}{w}}{({\rho})}}\right)}^{2}}}}}$;
${{{{{ {\partial \Gamma}}^{\phi}}_{\theta}}_{\phi}}_{\theta}} = {-{\frac{1}{{1} - {{cos\left( \theta\right)}^{2}}}}}$;
${{{{{ {\partial \Gamma}}^{\phi}}_{\phi}}_{\rho}}_{\rho}} = {\frac{{{({{sinh\left( {{\frac{1}{w}}{({\rho})}}\right)} - {cosh\left( {{\frac{1}{w}}{({\rho})}}\right)}})}} {{({{sinh\left( {{\frac{1}{w}}{({\rho})}}\right)} + {cosh\left( {{\frac{1}{w}}{({\rho})}}\right)}})}}}{{{{w}^{2}}} {{{sinh\left( {{\frac{1}{w}}{({\rho})}}\right)}^{2}}}}}$;
${{{{{ {\partial \Gamma}}^{\phi}}_{\phi}}_{\theta}}_{\theta}} = {-{\frac{1}{{1} - {{cos\left( \theta\right)}^{2}}}}}$
connection coefficients squared:
${{{{{ {(\Gamma^2)}}^{\rho}}_{\rho}}_{\rho}}_{\rho}} = {\frac{{sinh\left( {{\frac{1}{w}}{({\rho})}}\right)}^{2}}{{{{w}^{2}}} {{{cosh\left( {{\frac{1}{w}}{({\rho})}}\right)}^{2}}}}}$;
${{{{{ {(\Gamma^2)}}^{\rho}}_{\rho}}_{\theta}}_{\theta}} = {-{1}}$;
${{{{{ {(\Gamma^2)}}^{\rho}}_{\rho}}_{\phi}}_{\phi}} = {-{({{1} - {{cos\left( \theta\right)}^{2}}})}}$;
${{{{{ {(\Gamma^2)}}^{\rho}}_{\theta}}_{\rho}}_{\theta}} = {\frac{-{{sinh\left( {{\frac{1}{w}}{({\rho})}}\right)}^{2}}}{{cosh\left( {{\frac{1}{w}}{({\rho})}}\right)}^{2}}}$;
${{{{{ {(\Gamma^2)}}^{\rho}}_{\theta}}_{\theta}}_{\rho}} = {-{1}}$;
${{{{{ {(\Gamma^2)}}^{\rho}}_{\theta}}_{\phi}}_{\phi}} = {\frac{-{{{w}} {{sinh\left( {{\frac{1}{w}}{({\rho})}}\right)}} {{sin\left( \theta\right)}} {{cos\left( \theta\right)}}}}{cosh\left( {{\frac{1}{w}}{({\rho})}}\right)}}$;
${{{{{ {(\Gamma^2)}}^{\rho}}_{\phi}}_{\rho}}_{\phi}} = {\frac{{{{sinh\left( {{\frac{1}{w}}{({\rho})}}\right)}^{2}}} {{({{-{1}} + {{cos\left( \theta\right)}^{2}}})}}}{{cosh\left( {{\frac{1}{w}}{({\rho})}}\right)}^{2}}}$;
${{{{{ {(\Gamma^2)}}^{\rho}}_{\phi}}_{\theta}}_{\phi}} = {\frac{{{w}} {{sin\left( \theta\right)}} {{sinh\left( {{\frac{1}{w}}{({\rho})}}\right)}} {{cos\left( \theta\right)}}}{cosh\left( {{\frac{1}{w}}{({\rho})}}\right)}}$;
${{{{{ {(\Gamma^2)}}^{\rho}}_{\phi}}_{\phi}}_{\rho}} = {-{({{1} - {{cos\left( \theta\right)}^{2}}})}}$;
${{{{{ {(\Gamma^2)}}^{\rho}}_{\phi}}_{\phi}}_{\theta}} = {\frac{-{{{w}} {{sinh\left( {{\frac{1}{w}}{({\rho})}}\right)}} {{sin\left( \theta\right)}} {{cos\left( \theta\right)}}}}{cosh\left( {{\frac{1}{w}}{({\rho})}}\right)}}$;
${{{{{ {(\Gamma^2)}}^{\theta}}_{\rho}}_{\rho}}_{\theta}} = {\frac{{cosh\left( {{\frac{1}{w}}{({\rho})}}\right)}^{2}}{{{{w}^{2}}} {{{sinh\left( {{\frac{1}{w}}{({\rho})}}\right)}^{2}}}}}$;
${{{{{ {(\Gamma^2)}}^{\theta}}_{\rho}}_{\theta}}_{\rho}} = {\frac{1}{{w}^{2}}}$;
${{{{{ {(\Gamma^2)}}^{\theta}}_{\rho}}_{\phi}}_{\phi}} = {\frac{-{{{cosh\left( {{\frac{1}{w}}{({\rho})}}\right)}} {{sin\left( \theta\right)}} {{cos\left( \theta\right)}}}}{{{w}} {{sinh\left( {{\frac{1}{w}}{({\rho})}}\right)}}}}$;
${{{{{ {(\Gamma^2)}}^{\theta}}_{\theta}}_{\rho}}_{\rho}} = {\frac{{cosh\left( {{\frac{1}{w}}{({\rho})}}\right)}^{2}}{{{{w}^{2}}} {{{sinh\left( {{\frac{1}{w}}{({\rho})}}\right)}^{2}}}}}$;
${{{{{ {(\Gamma^2)}}^{\theta}}_{\theta}}_{\theta}}_{\theta}} = {-{1}}$;
${{{{{ {(\Gamma^2)}}^{\theta}}_{\theta}}_{\phi}}_{\phi}} = {-{{cos\left( \theta\right)}^{2}}}$;
${{{{{ {(\Gamma^2)}}^{\theta}}_{\phi}}_{\rho}}_{\phi}} = {\frac{-{{{cosh\left( {{\frac{1}{w}}{({\rho})}}\right)}} {{cos\left( \theta\right)}} {{sin\left( \theta\right)}}}}{{{w}} {{sinh\left( {{\frac{1}{w}}{({\rho})}}\right)}}}}$;
${{{{{ {(\Gamma^2)}}^{\theta}}_{\phi}}_{\theta}}_{\phi}} = {-{({{1} - {{cos\left( \theta\right)}^{2}}})}}$;
${{{{{ {(\Gamma^2)}}^{\theta}}_{\phi}}_{\phi}}_{\rho}} = {\frac{-{{{cosh\left( {{\frac{1}{w}}{({\rho})}}\right)}} {{sin\left( \theta\right)}} {{cos\left( \theta\right)}}}}{{{w}} {{sinh\left( {{\frac{1}{w}}{({\rho})}}\right)}}}}$;
${{{{{ {(\Gamma^2)}}^{\theta}}_{\phi}}_{\phi}}_{\theta}} = {-{{cos\left( \theta\right)}^{2}}}$;
${{{{{ {(\Gamma^2)}}^{\phi}}_{\rho}}_{\rho}}_{\phi}} = {\frac{{cosh\left( {{\frac{1}{w}}{({\rho})}}\right)}^{2}}{{{{w}^{2}}} {{{sinh\left( {{\frac{1}{w}}{({\rho})}}\right)}^{2}}}}}$;
${{{{{ {(\Gamma^2)}}^{\phi}}_{\rho}}_{\theta}}_{\phi}} = {\frac{{{cosh\left( {{\frac{1}{w}}{({\rho})}}\right)}} {{cos\left( \theta\right)}}}{{{w}} {{sinh\left( {{\frac{1}{w}}{({\rho})}}\right)}} {{sin\left( \theta\right)}}}}$;
${{{{{ {(\Gamma^2)}}^{\phi}}_{\rho}}_{\phi}}_{\rho}} = {\frac{1}{{w}^{2}}}$;
${{{{{ {(\Gamma^2)}}^{\phi}}_{\rho}}_{\phi}}_{\theta}} = {\frac{{{cos\left( \theta\right)}} {{cosh\left( {{\frac{1}{w}}{({\rho})}}\right)}}}{{{w}} {{sinh\left( {{\frac{1}{w}}{({\rho})}}\right)}} {{sin\left( \theta\right)}}}}$;
${{{{{ {(\Gamma^2)}}^{\phi}}_{\theta}}_{\rho}}_{\phi}} = {\frac{{{cos\left( \theta\right)}} {{cosh\left( {{\frac{1}{w}}{({\rho})}}\right)}}}{{{w}} {{sin\left( \theta\right)}} {{sinh\left( {{\frac{1}{w}}{({\rho})}}\right)}}}}$;
${{{{{ {(\Gamma^2)}}^{\phi}}_{\theta}}_{\theta}}_{\phi}} = {\frac{{cos\left( \theta\right)}^{2}}{{1} - {{cos\left( \theta\right)}^{2}}}}$;
${{{{{ {(\Gamma^2)}}^{\phi}}_{\theta}}_{\phi}}_{\rho}} = {\frac{{{cos\left( \theta\right)}} {{cosh\left( {{\frac{1}{w}}{({\rho})}}\right)}}}{{{w}} {{sinh\left( {{\frac{1}{w}}{({\rho})}}\right)}} {{sin\left( \theta\right)}}}}$;
${{{{{ {(\Gamma^2)}}^{\phi}}_{\theta}}_{\phi}}_{\theta}} = {-{1}}$;
${{{{{ {(\Gamma^2)}}^{\phi}}_{\phi}}_{\rho}}_{\rho}} = {\frac{{cosh\left( {{\frac{1}{w}}{({\rho})}}\right)}^{2}}{{{{w}^{2}}} {{{sinh\left( {{\frac{1}{w}}{({\rho})}}\right)}^{2}}}}}$;
${{{{{ {(\Gamma^2)}}^{\phi}}_{\phi}}_{\rho}}_{\theta}} = {\frac{{{cos\left( \theta\right)}} {{cosh\left( {{\frac{1}{w}}{({\rho})}}\right)}}}{{{w}} {{sin\left( \theta\right)}} {{sinh\left( {{\frac{1}{w}}{({\rho})}}\right)}}}}$;
${{{{{ {(\Gamma^2)}}^{\phi}}_{\phi}}_{\theta}}_{\rho}} = {\frac{{{cosh\left( {{\frac{1}{w}}{({\rho})}}\right)}} {{cos\left( \theta\right)}}}{{{w}} {{sinh\left( {{\frac{1}{w}}{({\rho})}}\right)}} {{sin\left( \theta\right)}}}}$;
${{{{{ {(\Gamma^2)}}^{\phi}}_{\phi}}_{\theta}}_{\theta}} = {\frac{{cos\left( \theta\right)}^{2}}{{1} - {{cos\left( \theta\right)}^{2}}}}$;
${{{{{ {(\Gamma^2)}}^{\phi}}_{\phi}}_{\phi}}_{\phi}} = {-{1}}$
Riemann curvature, $\sharp\flat\flat\flat$:
${{{{{ R}^a}_b}_c}_d} = {0}$
Riemann curvature, $\sharp\sharp\flat\flat$:
${{{{{ R}^a}^b}_c}_d} = {0}$
Ricci curvature, $\sharp\flat$:
${{{ R}^a}_b} = {0}$
Gaussian curvature:
$0$
trace-free Ricci, $\sharp\flat$:
${{{ {(R^{TF})}}^a}_b} = {0}$
Einstein / trace-reversed Ricci curvature, $\sharp\flat$:
${{{ G}^a}_b} = {0}$
Schouten, $\sharp\flat$:
${{{ P}^a}_b} = {0}$
Weyl, $\sharp\sharp\flat\flat$:
${{{{{ C}^a}^b}_c}_d} = {0}$
Weyl, $\flat\flat\flat\flat$:
${{{{{ C}_a}_b}_c}_d} = {0}$
Plebanski, $\sharp\sharp\flat\flat$:
${{{{{ P}^a}^b}_c}_d} = {0}$
divergence: ${{{{ A}^i}_{,i}} + {{{{{{ \Gamma}^i}_i}_j}} {{{ A}^j}}}} = {{\frac{\partial {A^{\rho}}}{\partial \rho}} + {\frac{\partial {A^{\theta}}}{\partial \theta}} + {\frac{\partial {A^{\phi}}}{\partial \phi}} + {{{{A^{\rho}}}} \cdot {{sinh\left( {{{\rho}} \cdot {{\frac{1}{w}}}}\right)}} {{\frac{1}{w}}} {{\frac{1}{cosh\left( {{{\rho}} \cdot {{\frac{1}{w}}}}\right)}}}} + {{{2}} {{{A^{\rho}}}} \cdot {{cosh\left( {{{\rho}} \cdot {{\frac{1}{w}}}}\right)}} {{\frac{1}{w}}} {{\frac{1}{sinh\left( {{{\rho}} \cdot {{\frac{1}{w}}}}\right)}}}} + {{{{A^{\theta}}}} \cdot {{cos\left( \theta\right)}} {{\frac{1}{sin\left( \theta\right)}}}}}$
geodesic:
${\overset{a\downarrow}{\left[\begin{matrix} \ddot{\rho} \\ \ddot{\theta} \\ \ddot{\phi}\end{matrix}\right]}} = {\overset{a\downarrow}{\left[\begin{matrix} {{{{\dot{\phi}}^{2}}} {{{w}^{2}}} {{sinh\left( {{{\rho}} \cdot {{\frac{1}{w}}}}\right)}} {{\frac{1}{w}}} {{\frac{1}{cosh\left( {{{\rho}} \cdot {{\frac{1}{w}}}}\right)}}}} + {{{-1}} {{{\dot{\phi}}^{2}}} {{{w}^{2}}} {{{cos\left( \theta\right)}^{2}}} {{sinh\left( {{{\rho}} \cdot {{\frac{1}{w}}}}\right)}} {{\frac{1}{w}}} {{\frac{1}{cosh\left( {{{\rho}} \cdot {{\frac{1}{w}}}}\right)}}}} + {{{-1}} {{{\dot{\rho}}^{2}}} {{sinh\left( {{{\rho}} \cdot {{\frac{1}{w}}}}\right)}} {{\frac{1}{w}}} {{\frac{1}{cosh\left( {{{\rho}} \cdot {{\frac{1}{w}}}}\right)}}}} + {{{{\dot{\theta}}^{2}}} {{{w}^{2}}} {{sinh\left( {{{\rho}} \cdot {{\frac{1}{w}}}}\right)}} {{\frac{1}{w}}} {{\frac{1}{cosh\left( {{{\rho}} \cdot {{\frac{1}{w}}}}\right)}}}} \\ {{{-2}} {{\dot{\rho}}} \cdot {{\dot{\theta}}} \cdot {{cosh\left( {{{\rho}} \cdot {{\frac{1}{w}}}}\right)}} {{\frac{1}{w}}} {{\frac{1}{sinh\left( {{{\rho}} \cdot {{\frac{1}{w}}}}\right)}}}} + {{{w}} {{{\dot{\phi}}^{2}}} {{sinh\left( {{{\rho}} \cdot {{\frac{1}{w}}}}\right)}} {{cos\left( \theta\right)}} {{sin\left( \theta\right)}} {{\frac{1}{w}}} {{\frac{1}{sinh\left( {{{\rho}} \cdot {{\frac{1}{w}}}}\right)}}}} \\ {{{-2}} {{\dot{\phi}}} \cdot {{\dot{\rho}}} \cdot {{sin\left( \theta\right)}} {{cosh\left( {{{\rho}} \cdot {{\frac{1}{w}}}}\right)}} {{\frac{1}{w}}} {{\frac{1}{sin\left( \theta\right)}}} {{\frac{1}{sinh\left( {{{\rho}} \cdot {{\frac{1}{w}}}}\right)}}}} + {{{-2}} {{\dot{\phi}}} \cdot {{\dot{\theta}}} \cdot {{w}} {{sinh\left( {{{\rho}} \cdot {{\frac{1}{w}}}}\right)}} {{cos\left( \theta\right)}} {{\frac{1}{w}}} {{\frac{1}{sin\left( \theta\right)}}} {{\frac{1}{sinh\left( {{{\rho}} \cdot {{\frac{1}{w}}}}\right)}}}}\end{matrix}\right]}}$
parallel propagators:
${{[\Gamma_\rho]}} = {\left[\begin{matrix} \frac{sinh\left( {{\frac{1}{w}}{({\rho})}}\right)}{{{w}} {{cosh\left( {{\frac{1}{w}}{({\rho})}}\right)}}} & 0 & 0 \\ 0 & \frac{cosh\left( {{\frac{1}{w}}{({\rho})}}\right)}{{{w}} {{sinh\left( {{\frac{1}{w}}{({\rho})}}\right)}}} & 0 \\ 0 & 0 & \frac{cosh\left( {{\frac{1}{w}}{({\rho})}}\right)}{{{w}} {{sinh\left( {{\frac{1}{w}}{({\rho})}}\right)}}}\end{matrix}\right]}$
$\int\limits_{{{\rho_L}}}^{{{\rho_R}}}d \rho\left( \left[\begin{matrix} \frac{sinh\left( {{\frac{1}{w}}{({\rho})}}\right)}{{{w}} {{cosh\left( {{\frac{1}{w}}{({\rho})}}\right)}}} & 0 & 0 \\ 0 & \frac{cosh\left( {{\frac{1}{w}}{({\rho})}}\right)}{{{w}} {{sinh\left( {{\frac{1}{w}}{({\rho})}}\right)}}} & 0 \\ 0 & 0 & \frac{cosh\left( {{\frac{1}{w}}{({\rho})}}\right)}{{{w}} {{sinh\left( {{\frac{1}{w}}{({\rho})}}\right)}}}\end{matrix}\right]\right)$
= $\left[\begin{matrix} log\left( {\frac{cosh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)}{cosh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}}\right) & 0 & 0 \\ 0 & log\left( {\frac{|{sinh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)}|}{|{sinh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}|}}\right) & 0 \\ 0 & 0 & log\left( {\frac{|{sinh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)}|}{|{sinh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}|}}\right)\end{matrix}\right]$
${ P}_{\rho}$ = ${e}^{( -{({\int\limits_{{{\rho_L}}}^{{{\rho_R}}}d \rho\left( \left[\begin{matrix} \frac{sinh\left( {{\frac{1}{w}}{({\rho})}}\right)}{{{w}} {{cosh\left( {{\frac{1}{w}}{({\rho})}}\right)}}} & 0 & 0 \\ 0 & \frac{cosh\left( {{\frac{1}{w}}{({\rho})}}\right)}{{{w}} {{sinh\left( {{\frac{1}{w}}{({\rho})}}\right)}}} & 0 \\ 0 & 0 & \frac{cosh\left( {{\frac{1}{w}}{({\rho})}}\right)}{{{w}} {{sinh\left( {{\frac{1}{w}}{({\rho})}}\right)}}}\end{matrix}\right]\right)})})}$
= $\left[\begin{matrix} \frac{cosh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}{cosh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)} & 0 & 0 \\ 0 & \frac{|{sinh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}|}{|{sinh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)}|} & 0 \\ 0 & 0 & \frac{|{sinh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}|}{|{sinh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)}|}\end{matrix}\right]$
${{ P}_{\rho}}^{-1}$ = ${e}^{({\int\limits_{{{\rho_L}}}^{{{\rho_R}}}d \rho\left( \left[\begin{matrix} \frac{sinh\left( {{\frac{1}{w}}{({\rho})}}\right)}{{{w}} {{cosh\left( {{\frac{1}{w}}{({\rho})}}\right)}}} & 0 & 0 \\ 0 & \frac{cosh\left( {{\frac{1}{w}}{({\rho})}}\right)}{{{w}} {{sinh\left( {{\frac{1}{w}}{({\rho})}}\right)}}} & 0 \\ 0 & 0 & \frac{cosh\left( {{\frac{1}{w}}{({\rho})}}\right)}{{{w}} {{sinh\left( {{\frac{1}{w}}{({\rho})}}\right)}}}\end{matrix}\right]\right)})}$
= $\left[\begin{matrix} \frac{cosh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)}{cosh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)} & 0 & 0 \\ 0 & \frac{|{sinh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)}|}{|{sinh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}|} & 0 \\ 0 & 0 & \frac{|{sinh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)}|}{|{sinh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}|}\end{matrix}\right]$
${{[\Gamma_\theta]}} = {\left[\begin{matrix} 0 & \frac{-{{{w}} {{sinh\left( {{\frac{1}{w}}{({\rho})}}\right)}}}}{cosh\left( {{\frac{1}{w}}{({\rho})}}\right)} & 0 \\ \frac{cosh\left( {{\frac{1}{w}}{({\rho})}}\right)}{{{w}} {{sinh\left( {{\frac{1}{w}}{({\rho})}}\right)}}} & 0 & 0 \\ 0 & 0 & \frac{cos\left( \theta\right)}{sin\left( \theta\right)}\end{matrix}\right]}$
$\int\limits_{{{\theta_L}}}^{{{\theta_R}}}d \theta\left( \left[\begin{matrix} 0 & \frac{-{{{w}} {{sinh\left( {{\frac{1}{w}}{({\rho})}}\right)}}}}{cosh\left( {{\frac{1}{w}}{({\rho})}}\right)} & 0 \\ \frac{cosh\left( {{\frac{1}{w}}{({\rho})}}\right)}{{{w}} {{sinh\left( {{\frac{1}{w}}{({\rho})}}\right)}}} & 0 & 0 \\ 0 & 0 & \frac{cos\left( \theta\right)}{sin\left( \theta\right)}\end{matrix}\right]\right)$
= $\left[\begin{matrix} 0 & \frac{-{{{w}} {{sinh\left( {{\frac{1}{w}}{({\rho})}}\right)}} {{({{{\theta_R}} - {{\theta_L}}})}}}}{cosh\left( {{\frac{1}{w}}{({\rho})}}\right)} & 0 \\ \frac{-{{{cosh\left( {{\frac{1}{w}}{({\rho})}}\right)}} {{({{{\theta_L}} - {{\theta_R}}})}}}}{{{w}} {{sinh\left( {{\frac{1}{w}}{({\rho})}}\right)}}} & 0 & 0 \\ 0 & 0 & log\left( {\frac{|{sin\left( {\theta_R}\right)}|}{|{sin\left( {\theta_L}\right)}|}}\right)\end{matrix}\right]$
${ P}_{\theta}$ = ${e}^{( -{({\int\limits_{{{\theta_L}}}^{{{\theta_R}}}d \theta\left( \left[\begin{matrix} 0 & \frac{-{{{w}} {{sinh\left( {{\frac{1}{w}}{({\rho})}}\right)}}}}{cosh\left( {{\frac{1}{w}}{({\rho})}}\right)} & 0 \\ \frac{cosh\left( {{\frac{1}{w}}{({\rho})}}\right)}{{{w}} {{sinh\left( {{\frac{1}{w}}{({\rho})}}\right)}}} & 0 & 0 \\ 0 & 0 & \frac{cos\left( \theta\right)}{sin\left( \theta\right)}\end{matrix}\right]\right)})})}$
= $\left[\begin{matrix} cos\left( {{{\theta_L}} - {{\theta_R}}}\right) & \frac{-{{{w}} {{sin\left( {{{\theta_L}} - {{\theta_R}}}\right)}} {{sinh\left( {{\frac{1}{w}}{({\rho})}}\right)}}}}{cosh\left( {{\frac{1}{w}}{({\rho})}}\right)} & 0 \\ \frac{{{cosh\left( {{\frac{1}{w}}{({\rho})}}\right)}} {{sin\left( {{{\theta_L}} - {{\theta_R}}}\right)}}}{{{w}} {{sinh\left( {{\frac{1}{w}}{({\rho})}}\right)}}} & cos\left( {{{\theta_L}} - {{\theta_R}}}\right) & 0 \\ 0 & 0 & \frac{|{sin\left( {\theta_L}\right)}|}{|{sin\left( {\theta_R}\right)}|}\end{matrix}\right]$
${{ P}_{\theta}}^{-1}$ = ${e}^{({\int\limits_{{{\theta_L}}}^{{{\theta_R}}}d \theta\left( \left[\begin{matrix} 0 & \frac{-{{{w}} {{sinh\left( {{\frac{1}{w}}{({\rho})}}\right)}}}}{cosh\left( {{\frac{1}{w}}{({\rho})}}\right)} & 0 \\ \frac{cosh\left( {{\frac{1}{w}}{({\rho})}}\right)}{{{w}} {{sinh\left( {{\frac{1}{w}}{({\rho})}}\right)}}} & 0 & 0 \\ 0 & 0 & \frac{cos\left( \theta\right)}{sin\left( \theta\right)}\end{matrix}\right]\right)})}$
= $\left[\begin{matrix} cos\left( {{{\theta_L}} - {{\theta_R}}}\right) & \frac{{{w}} {{sinh\left( {{\frac{1}{w}}{({\rho})}}\right)}} {{sin\left( {{{\theta_L}} - {{\theta_R}}}\right)}}}{cosh\left( {{\frac{1}{w}}{({\rho})}}\right)} & 0 \\ \frac{{{cosh\left( {{\frac{1}{w}}{({\rho})}}\right)}} {{sin\left( {{{\theta_L}} - {{\theta_R}}}\right)}}}{-{{{w}} {{sinh\left( {{\frac{1}{w}}{({\rho})}}\right)}}}} & cos\left( {{{\theta_L}} - {{\theta_R}}}\right) & 0 \\ 0 & 0 & \frac{|{sin\left( {\theta_R}\right)}|}{|{sin\left( {\theta_L}\right)}|}\end{matrix}\right]$
${{[\Gamma_\phi]}} = {\left[\begin{matrix} 0 & 0 & \frac{{{w}} {{sinh\left( {{\frac{1}{w}}{({\rho})}}\right)}} {{({{-{1}} + {{cos\left( \theta\right)}^{2}}})}}}{cosh\left( {{\frac{1}{w}}{({\rho})}}\right)} \\ 0 & 0 & -{{{cos\left( \theta\right)}} {{sin\left( \theta\right)}}} \\ \frac{cosh\left( {{\frac{1}{w}}{({\rho})}}\right)}{{{w}} {{sinh\left( {{\frac{1}{w}}{({\rho})}}\right)}}} & \frac{cos\left( \theta\right)}{sin\left( \theta\right)} & 0\end{matrix}\right]}$
$\int\limits_{{{\phi_L}}}^{{{\phi_R}}}d \phi\left( \left[\begin{matrix} 0 & 0 & \frac{{{w}} {{sinh\left( {{\frac{1}{w}}{({\rho})}}\right)}} {{({{-{1}} + {{cos\left( \theta\right)}^{2}}})}}}{cosh\left( {{\frac{1}{w}}{({\rho})}}\right)} \\ 0 & 0 & -{{{cos\left( \theta\right)}} {{sin\left( \theta\right)}}} \\ \frac{cosh\left( {{\frac{1}{w}}{({\rho})}}\right)}{{{w}} {{sinh\left( {{\frac{1}{w}}{({\rho})}}\right)}}} & \frac{cos\left( \theta\right)}{sin\left( \theta\right)} & 0\end{matrix}\right]\right)$
= $\left[\begin{matrix} 0 & 0 & \frac{-{{{w}} {{sinh\left( {{\frac{1}{w}}{({\rho})}}\right)}} {{({{{{{{{\phi_L}}} \cdot {{{cos\left( \theta\right)}^{2}}}} - {{\phi_L}}} - {{{{\phi_R}}} \cdot {{{cos\left( \theta\right)}^{2}}}}} + {{\phi_R}}})}}}}{cosh\left( {{\frac{1}{w}}{({\rho})}}\right)} \\ 0 & 0 & -{{{sin\left( \theta\right)}} {{cos\left( \theta\right)}} {{({{{\phi_R}} - {{\phi_L}}})}}} \\ \frac{-{{{cosh\left( {{\frac{1}{w}}{({\rho})}}\right)}} {{({{{\phi_L}} - {{\phi_R}}})}}}}{{{w}} {{sinh\left( {{\frac{1}{w}}{({\rho})}}\right)}}} & \frac{-{{{cos\left( \theta\right)}} {{({{{\phi_L}} - {{\phi_R}}})}}}}{sin\left( \theta\right)} & 0\end{matrix}\right]$
${ P}_{\phi}$ = ${e}^{( -{({\int\limits_{{{\phi_L}}}^{{{\phi_R}}}d \phi\left( \left[\begin{matrix} 0 & 0 & \frac{{{w}} {{sinh\left( {{\frac{1}{w}}{({\rho})}}\right)}} {{({{-{1}} + {{cos\left( \theta\right)}^{2}}})}}}{cosh\left( {{\frac{1}{w}}{({\rho})}}\right)} \\ 0 & 0 & -{{{cos\left( \theta\right)}} {{sin\left( \theta\right)}}} \\ \frac{cosh\left( {{\frac{1}{w}}{({\rho})}}\right)}{{{w}} {{sinh\left( {{\frac{1}{w}}{({\rho})}}\right)}}} & \frac{cos\left( \theta\right)}{sin\left( \theta\right)} & 0\end{matrix}\right]\right)})})}$
= ${\left[\begin{matrix} {\frac{1}{2}}{({-{({{{{{\phi_L}}^{2}} - {{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}} \cdot {{{cos\left( \theta\right)}^{2}}}} - {{{{{\phi_L}}^{2}}} {{{cos\left( \theta\right)}^{2}}}}} + {{{{\phi_R}}^{2}} - {{{{{\phi_R}}^{2}}} {{{cos\left( \theta\right)}^{2}}}}}})}})} & \frac{{{w}} {{({{{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_L}}^{2}}} - {{{\phi_R}}^{2}}})}} {{sin\left( \theta\right)}} {{cos\left( \theta\right)}} {{sinh\left( {{\frac{1}{w}}{({\rho})}}\right)}}}{{{2}} {{cosh\left( {{\frac{1}{w}}{({\rho})}}\right)}}} & \frac{{{w}} {{sinh\left( {{\frac{1}{w}}{({\rho})}}\right)}} {{({{{{{3}} {{{\phi_L}}} \cdot {{{{\phi_R}}^{2}}} {{{cos\left( \theta\right)}^{4}}}} - {{{9}} {{{\phi_L}}} \cdot {{{{\phi_R}}^{2}}} {{{cos\left( \theta\right)}^{2}}}}} + {{{{3}} {{{\phi_L}}} \cdot {{{{\phi_R}}^{2}}} {{{cos\left( \theta\right)}^{2}}} {{{sin\left( \theta\right)}^{2}}}} - {{{3}} {{{\phi_L}}} \cdot {{{{\phi_R}}^{2}}} {{{sin\left( \theta\right)}^{2}}}}} + {{{6}} {{{\phi_L}}} \cdot {{{{\phi_R}}^{2}}}} + {{{{{6}} {{{\phi_L}}} \cdot {{{cos\left( \theta\right)}^{2}}}} - {{{6}} {{{\phi_L}}}}} - {{{3}} {{{\phi_R}}} \cdot {{{{\phi_L}}^{2}}} {{{cos\left( \theta\right)}^{4}}}}} + {{{{9}} {{{\phi_R}}} \cdot {{{{\phi_L}}^{2}}} {{{cos\left( \theta\right)}^{2}}}} - {{{3}} {{{\phi_R}}} \cdot {{{{\phi_L}}^{2}}} {{{cos\left( \theta\right)}^{2}}} {{{sin\left( \theta\right)}^{2}}}}} + {{{{{3}} {{{\phi_R}}} \cdot {{{{\phi_L}}^{2}}} {{{sin\left( \theta\right)}^{2}}}} - {{{6}} {{{\phi_R}}} \cdot {{{{\phi_L}}^{2}}}}} - {{{6}} {{{\phi_R}}} \cdot {{{cos\left( \theta\right)}^{2}}}}} + {{{6}} {{{\phi_R}}}} + {{{{{\phi_L}}^{3}}} {{{cos\left( \theta\right)}^{2}}} {{{sin\left( \theta\right)}^{2}}}} + {{{{{{{\phi_L}}^{3}}} {{{cos\left( \theta\right)}^{4}}}} - {{{3}} {{{{\phi_L}}^{3}}} {{{cos\left( \theta\right)}^{2}}}}} - {{{{{\phi_L}}^{3}}} {{{sin\left( \theta\right)}^{2}}}}} + {{{2}} {{{{\phi_L}}^{3}}}} + {{{{{3}} {{{{\phi_R}}^{3}}} {{{cos\left( \theta\right)}^{2}}}} - {{{{{\phi_R}}^{3}}} {{{cos\left( \theta\right)}^{4}}}}} - {{{{{\phi_R}}^{3}}} {{{sin\left( \theta\right)}^{2}}} {{{cos\left( \theta\right)}^{2}}}}} + {{{{{{\phi_R}}^{3}}} {{{sin\left( \theta\right)}^{2}}}} - {{{2}} {{{{\phi_R}}^{3}}}}}})}}}{{{6}} {{cosh\left( {{\frac{1}{w}}{({\rho})}}\right)}}} \\ \frac{-{{{{({{{\phi_L}} - {{\phi_R}}})}^{2}}} {{sin\left( \theta\right)}} {{cos\left( \theta\right)}} {{cosh\left( {{\frac{1}{w}}{({\rho})}}\right)}}}}{{{2}} {{w}} {{sinh\left( {{\frac{1}{w}}{({\rho})}}\right)}}} & {\frac{1}{2}}{({{{{cos\left( \theta\right)}^{2}}} {{({{{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_L}}^{2}}} - {{{\phi_R}}^{2}}})}}})} & {\frac{1}{6}}{({{{sin\left( \theta\right)}} {{cos\left( \theta\right)}} {{({{{{{{3}} {{{\phi_L}}} \cdot {{{{\phi_R}}^{2}}}} - {{{6}} {{{\phi_L}}}}} - {{{3}} {{{\phi_R}}} \cdot {{{{\phi_L}}^{2}}}}} + {{{{6}} {{{\phi_R}}}} - {{{\phi_R}}^{3}}} + {{{\phi_L}}^{3}}})}}})} \\ \frac{-{{{cosh\left( {{\frac{1}{w}}{({\rho})}}\right)}} {{({{{{3}} {{{\phi_L}}} \cdot {{{{\phi_R}}^{2}}}} + {{{{{\phi_L}}^{3}} - {{{6}} {{{\phi_L}}}}} - {{{3}} {{{\phi_R}}} \cdot {{{{\phi_L}}^{2}}}}} + {{{{6}} {{{\phi_R}}}} - {{{\phi_R}}^{3}}}})}}}}{{{6}} {{w}} {{sinh\left( {{\frac{1}{w}}{({\rho})}}\right)}}} & \frac{-{{{cos\left( \theta\right)}} {{({{{{3}} {{{\phi_L}}} \cdot {{{{\phi_R}}^{2}}}} + {{{{{\phi_L}}^{3}} - {{{6}} {{{\phi_L}}}}} - {{{3}} {{{\phi_R}}} \cdot {{{{\phi_L}}^{2}}}}} + {{{{6}} {{{\phi_R}}}} - {{{\phi_R}}^{3}}}})}}}}{{{6}} {{sin\left( \theta\right)}}} & {\frac{1}{2}}{({-{({{{{{\phi_L}}^{2}} - {{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}}} + {{{\phi_R}}^{2}}})}})}\end{matrix}\right]} + {{\mathcal{O}(A^4)}}$
${{ P}_{\phi}}^{-1}$ = ${e}^{({\int\limits_{{{\phi_L}}}^{{{\phi_R}}}d \phi\left( \left[\begin{matrix} 0 & 0 & \frac{{{w}} {{sinh\left( {{\frac{1}{w}}{({\rho})}}\right)}} {{({{-{1}} + {{cos\left( \theta\right)}^{2}}})}}}{cosh\left( {{\frac{1}{w}}{({\rho})}}\right)} \\ 0 & 0 & -{{{cos\left( \theta\right)}} {{sin\left( \theta\right)}}} \\ \frac{cosh\left( {{\frac{1}{w}}{({\rho})}}\right)}{{{w}} {{sinh\left( {{\frac{1}{w}}{({\rho})}}\right)}}} & \frac{cos\left( \theta\right)}{sin\left( \theta\right)} & 0\end{matrix}\right]\right)})}$
= ${\left[\begin{matrix} {\frac{1}{2}}{({-{({{{{{\phi_L}}^{2}} - {{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}} \cdot {{{cos\left( \theta\right)}^{2}}}} - {{{{{\phi_L}}^{2}}} {{{cos\left( \theta\right)}^{2}}}}} + {{{{\phi_R}}^{2}} - {{{{{\phi_R}}^{2}}} {{{cos\left( \theta\right)}^{2}}}}}})}})} & \frac{{{w}} {{({{{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_L}}^{2}}} - {{{\phi_R}}^{2}}})}} {{sin\left( \theta\right)}} {{cos\left( \theta\right)}} {{sinh\left( {{\frac{1}{w}}{({\rho})}}\right)}}}{{{2}} {{cosh\left( {{\frac{1}{w}}{({\rho})}}\right)}}} & \frac{-{{{w}} {{sinh\left( {{\frac{1}{w}}{({\rho})}}\right)}} {{({{{{{3}} {{{\phi_L}}} \cdot {{{{\phi_R}}^{2}}} {{{cos\left( \theta\right)}^{4}}}} - {{{9}} {{{\phi_L}}} \cdot {{{{\phi_R}}^{2}}} {{{cos\left( \theta\right)}^{2}}}}} + {{{{3}} {{{\phi_L}}} \cdot {{{{\phi_R}}^{2}}} {{{cos\left( \theta\right)}^{2}}} {{{sin\left( \theta\right)}^{2}}}} - {{{3}} {{{\phi_L}}} \cdot {{{{\phi_R}}^{2}}} {{{sin\left( \theta\right)}^{2}}}}} + {{{6}} {{{\phi_L}}} \cdot {{{{\phi_R}}^{2}}}} + {{{{{6}} {{{\phi_L}}} \cdot {{{cos\left( \theta\right)}^{2}}}} - {{{6}} {{{\phi_L}}}}} - {{{3}} {{{\phi_R}}} \cdot {{{{\phi_L}}^{2}}} {{{cos\left( \theta\right)}^{4}}}}} + {{{{9}} {{{\phi_R}}} \cdot {{{{\phi_L}}^{2}}} {{{cos\left( \theta\right)}^{2}}}} - {{{3}} {{{\phi_R}}} \cdot {{{{\phi_L}}^{2}}} {{{cos\left( \theta\right)}^{2}}} {{{sin\left( \theta\right)}^{2}}}}} + {{{{{3}} {{{\phi_R}}} \cdot {{{{\phi_L}}^{2}}} {{{sin\left( \theta\right)}^{2}}}} - {{{6}} {{{\phi_R}}} \cdot {{{{\phi_L}}^{2}}}}} - {{{6}} {{{\phi_R}}} \cdot {{{cos\left( \theta\right)}^{2}}}}} + {{{6}} {{{\phi_R}}}} + {{{{{\phi_L}}^{3}}} {{{cos\left( \theta\right)}^{2}}} {{{sin\left( \theta\right)}^{2}}}} + {{{{{{{\phi_L}}^{3}}} {{{cos\left( \theta\right)}^{4}}}} - {{{3}} {{{{\phi_L}}^{3}}} {{{cos\left( \theta\right)}^{2}}}}} - {{{{{\phi_L}}^{3}}} {{{sin\left( \theta\right)}^{2}}}}} + {{{2}} {{{{\phi_L}}^{3}}}} + {{{{{3}} {{{{\phi_R}}^{3}}} {{{cos\left( \theta\right)}^{2}}}} - {{{{{\phi_R}}^{3}}} {{{cos\left( \theta\right)}^{4}}}}} - {{{{{\phi_R}}^{3}}} {{{sin\left( \theta\right)}^{2}}} {{{cos\left( \theta\right)}^{2}}}}} + {{{{{{\phi_R}}^{3}}} {{{sin\left( \theta\right)}^{2}}}} - {{{2}} {{{{\phi_R}}^{3}}}}}})}}}}{{{6}} {{cosh\left( {{\frac{1}{w}}{({\rho})}}\right)}}} \\ \frac{{{({{{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_L}}^{2}}} - {{{\phi_R}}^{2}}})}} {{sin\left( \theta\right)}} {{cos\left( \theta\right)}} {{cosh\left( {{\frac{1}{w}}{({\rho})}}\right)}}}{{{2}} {{w}} {{sinh\left( {{\frac{1}{w}}{({\rho})}}\right)}}} & {\frac{1}{2}}{({{{{cos\left( \theta\right)}^{2}}} {{({{{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_L}}^{2}}} - {{{\phi_R}}^{2}}})}}})} & {\frac{1}{6}}{({-{{{cos\left( \theta\right)}} {{sin\left( \theta\right)}} {{({{{{{3}} {{{\phi_L}}} \cdot {{{{\phi_R}}^{2}}}} - {{{6}} {{{\phi_L}}}}} + {{{{\phi_L}}^{3}} - {{{3}} {{{\phi_R}}} \cdot {{{{\phi_L}}^{2}}}}} + {{{{6}} {{{\phi_R}}}} - {{{\phi_R}}^{3}}}})}}}})} \\ \frac{{{cosh\left( {{\frac{1}{w}}{({\rho})}}\right)}} {{({{{{3}} {{{\phi_L}}} \cdot {{{{\phi_R}}^{2}}}} + {{{{{\phi_L}}^{3}} - {{{6}} {{{\phi_L}}}}} - {{{3}} {{{\phi_R}}} \cdot {{{{\phi_L}}^{2}}}}} + {{{{6}} {{{\phi_R}}}} - {{{\phi_R}}^{3}}}})}}}{{{6}} {{w}} {{sinh\left( {{\frac{1}{w}}{({\rho})}}\right)}}} & \frac{{{cos\left( \theta\right)}} {{({{{{3}} {{{\phi_L}}} \cdot {{{{\phi_R}}^{2}}}} + {{{{{\phi_L}}^{3}} - {{{6}} {{{\phi_L}}}}} - {{{3}} {{{\phi_R}}} \cdot {{{{\phi_L}}^{2}}}}} + {{{{6}} {{{\phi_R}}}} - {{{\phi_R}}^{3}}}})}}}{{{6}} {{sin\left( \theta\right)}}} & {\frac{1}{2}}{({-{({{{{{\phi_L}}^{2}} - {{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}}} + {{{\phi_R}}^{2}}})}})}\end{matrix}\right]} + {{\mathcal{O}(A^4)}}$
propagator commutation:
[ ${ P}_{\rho}$ , ${ P}_{\theta}$ ] = ${ {\left[\begin{matrix} \frac{cosh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}{cosh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)} & 0 & 0 \\ 0 & \frac{|{sinh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}|}{|{sinh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)}|} & 0 \\ 0 & 0 & \frac{|{sinh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}|}{|{sinh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)}|}\end{matrix}\right]} {\left[\begin{matrix} cos\left( {{{\theta_L}} - {{\theta_R}}}\right) & \frac{-{{{w}} {{sin\left( {{{\theta_L}} - {{\theta_R}}}\right)}} {{sinh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}}}}{cosh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)} & 0 \\ \frac{{{cosh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}} {{sin\left( {{{\theta_L}} - {{\theta_R}}}\right)}}}{{{w}} {{sinh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}}} & cos\left( {{{\theta_L}} - {{\theta_R}}}\right) & 0 \\ 0 & 0 & \frac{|{sin\left( {\theta_L}\right)}|}{|{sin\left( {\theta_R}\right)}|}\end{matrix}\right]}} - { {\left[\begin{matrix} cos\left( {{{\theta_L}} - {{\theta_R}}}\right) & \frac{-{{{w}} {{sin\left( {{{\theta_L}} - {{\theta_R}}}\right)}} {{sinh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)}}}}{cosh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)} & 0 \\ \frac{{{cosh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)}} {{sin\left( {{{\theta_L}} - {{\theta_R}}}\right)}}}{{{w}} {{sinh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)}}} & cos\left( {{{\theta_L}} - {{\theta_R}}}\right) & 0 \\ 0 & 0 & \frac{|{sin\left( {\theta_L}\right)}|}{|{sin\left( {\theta_R}\right)}|}\end{matrix}\right]} {\left[\begin{matrix} \frac{cosh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}{cosh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)} & 0 & 0 \\ 0 & \frac{|{sinh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}|}{|{sinh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)}|} & 0 \\ 0 & 0 & \frac{|{sinh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}|}{|{sinh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)}|}\end{matrix}\right]}}$ = $\left[\begin{matrix} 0 & \frac{{{w}} {{sin\left( {{{\theta_L}} - {{\theta_R}}}\right)}} {{({{{{|{sinh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}|}} {{sinh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)}}} - {{{sinh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}} {{|{sinh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)}|}}}})}}}{{{cosh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)}} {{|{sinh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)}|}}} & 0 \\ \frac{{{cosh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}} {{sin\left( {{{\theta_L}} - {{\theta_R}}}\right)}} {{({{{{|{sinh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}|}} {{sinh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)}}} - {{{sinh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}} {{|{sinh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)}|}}}})}}}{{{w}} {{|{sinh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)}|}} {{sinh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}} {{sinh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)}}} & 0 & 0 \\ 0 & 0 & 0\end{matrix}\right]$
[ ${ P}_{\rho}$ , ${ P}_{\phi}$ ] = ${ {\left[\begin{matrix} \frac{cosh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}{cosh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)} & 0 & 0 \\ 0 & \frac{|{sinh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}|}{|{sinh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)}|} & 0 \\ 0 & 0 & \frac{|{sinh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}|}{|{sinh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)}|}\end{matrix}\right]} {{({{\left[\begin{matrix} {\frac{1}{2}}{({-{({{{{{\phi_L}}^{2}} - {{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}} \cdot {{{cos\left( {\theta_L}\right)}^{2}}}} - {{{{{\phi_L}}^{2}}} {{{cos\left( {\theta_L}\right)}^{2}}}}} + {{{{\phi_R}}^{2}} - {{{{{\phi_R}}^{2}}} {{{cos\left( {\theta_L}\right)}^{2}}}}}})}})} & \frac{{{w}} {{({{{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_L}}^{2}}} - {{{\phi_R}}^{2}}})}} {{sin\left( {\theta_L}\right)}} {{cos\left( {\theta_L}\right)}} {{sinh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}}}{{{2}} {{cosh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}}} & \frac{{{w}} {{sinh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}} {{({{{{{3}} {{{\phi_L}}} \cdot {{{{\phi_R}}^{2}}} {{{cos\left( {\theta_L}\right)}^{4}}}} - {{{9}} {{{\phi_L}}} \cdot {{{{\phi_R}}^{2}}} {{{cos\left( {\theta_L}\right)}^{2}}}}} + {{{{3}} {{{\phi_L}}} \cdot {{{{\phi_R}}^{2}}} {{{cos\left( {\theta_L}\right)}^{2}}} {{{sin\left( {\theta_L}\right)}^{2}}}} - {{{3}} {{{\phi_L}}} \cdot {{{{\phi_R}}^{2}}} {{{sin\left( {\theta_L}\right)}^{2}}}}} + {{{6}} {{{\phi_L}}} \cdot {{{{\phi_R}}^{2}}}} + {{{{{6}} {{{\phi_L}}} \cdot {{{cos\left( {\theta_L}\right)}^{2}}}} - {{{6}} {{{\phi_L}}}}} - {{{3}} {{{\phi_R}}} \cdot {{{{\phi_L}}^{2}}} {{{cos\left( {\theta_L}\right)}^{4}}}}} + {{{{9}} {{{\phi_R}}} \cdot {{{{\phi_L}}^{2}}} {{{cos\left( {\theta_L}\right)}^{2}}}} - {{{3}} {{{\phi_R}}} \cdot {{{{\phi_L}}^{2}}} {{{cos\left( {\theta_L}\right)}^{2}}} {{{sin\left( {\theta_L}\right)}^{2}}}}} + {{{{{3}} {{{\phi_R}}} \cdot {{{{\phi_L}}^{2}}} {{{sin\left( {\theta_L}\right)}^{2}}}} - {{{6}} {{{\phi_R}}} \cdot {{{{\phi_L}}^{2}}}}} - {{{6}} {{{\phi_R}}} \cdot {{{cos\left( {\theta_L}\right)}^{2}}}}} + {{{6}} {{{\phi_R}}}} + {{{{{\phi_L}}^{3}}} {{{cos\left( {\theta_L}\right)}^{2}}} {{{sin\left( {\theta_L}\right)}^{2}}}} + {{{{{{{\phi_L}}^{3}}} {{{cos\left( {\theta_L}\right)}^{4}}}} - {{{3}} {{{{\phi_L}}^{3}}} {{{cos\left( {\theta_L}\right)}^{2}}}}} - {{{{{\phi_L}}^{3}}} {{{sin\left( {\theta_L}\right)}^{2}}}}} + {{{2}} {{{{\phi_L}}^{3}}}} + {{{{{3}} {{{{\phi_R}}^{3}}} {{{cos\left( {\theta_L}\right)}^{2}}}} - {{{{{\phi_R}}^{3}}} {{{cos\left( {\theta_L}\right)}^{4}}}}} - {{{{{\phi_R}}^{3}}} {{{sin\left( {\theta_L}\right)}^{2}}} {{{cos\left( {\theta_L}\right)}^{2}}}}} + {{{{{{\phi_R}}^{3}}} {{{sin\left( {\theta_L}\right)}^{2}}}} - {{{2}} {{{{\phi_R}}^{3}}}}}})}}}{{{6}} {{cosh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}}} \\ \frac{-{{{{({{{\phi_L}} - {{\phi_R}}})}^{2}}} {{sin\left( {\theta_L}\right)}} {{cos\left( {\theta_L}\right)}} {{cosh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}}}}{{{2}} {{w}} {{sinh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}}} & {\frac{1}{2}}{({{{{cos\left( {\theta_L}\right)}^{2}}} {{({{{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_L}}^{2}}} - {{{\phi_R}}^{2}}})}}})} & {\frac{1}{6}}{({{{sin\left( {\theta_L}\right)}} {{cos\left( {\theta_L}\right)}} {{({{{{{{3}} {{{\phi_L}}} \cdot {{{{\phi_R}}^{2}}}} - {{{6}} {{{\phi_L}}}}} - {{{3}} {{{\phi_R}}} \cdot {{{{\phi_L}}^{2}}}}} + {{{{6}} {{{\phi_R}}}} - {{{\phi_R}}^{3}}} + {{{\phi_L}}^{3}}})}}})} \\ \frac{-{{{cosh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}} {{({{{{3}} {{{\phi_L}}} \cdot {{{{\phi_R}}^{2}}}} + {{{{{\phi_L}}^{3}} - {{{6}} {{{\phi_L}}}}} - {{{3}} {{{\phi_R}}} \cdot {{{{\phi_L}}^{2}}}}} + {{{{6}} {{{\phi_R}}}} - {{{\phi_R}}^{3}}}})}}}}{{{6}} {{w}} {{sinh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}}} & \frac{-{{{cos\left( {\theta_L}\right)}} {{({{{{3}} {{{\phi_L}}} \cdot {{{{\phi_R}}^{2}}}} + {{{{{\phi_L}}^{3}} - {{{6}} {{{\phi_L}}}}} - {{{3}} {{{\phi_R}}} \cdot {{{{\phi_L}}^{2}}}}} + {{{{6}} {{{\phi_R}}}} - {{{\phi_R}}^{3}}}})}}}}{{{6}} {{sin\left( {\theta_L}\right)}}} & {\frac{1}{2}}{({-{({{{{{\phi_L}}^{2}} - {{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}}} + {{{\phi_R}}^{2}}})}})}\end{matrix}\right]} + {{\mathcal{O}(A^4)}}})}}} - {{{({{\left[\begin{matrix} {\frac{1}{2}}{({-{({{{{{\phi_L}}^{2}} - {{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}} \cdot {{{cos\left( {\theta_L}\right)}^{2}}}} - {{{{{\phi_L}}^{2}}} {{{cos\left( {\theta_L}\right)}^{2}}}}} + {{{{\phi_R}}^{2}} - {{{{{\phi_R}}^{2}}} {{{cos\left( {\theta_L}\right)}^{2}}}}}})}})} & \frac{{{w}} {{({{{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_L}}^{2}}} - {{{\phi_R}}^{2}}})}} {{sin\left( {\theta_L}\right)}} {{cos\left( {\theta_L}\right)}} {{sinh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)}}}{{{2}} {{cosh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)}}} & \frac{{{w}} {{sinh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)}} {{({{{{{3}} {{{\phi_L}}} \cdot {{{{\phi_R}}^{2}}} {{{cos\left( {\theta_L}\right)}^{4}}}} - {{{9}} {{{\phi_L}}} \cdot {{{{\phi_R}}^{2}}} {{{cos\left( {\theta_L}\right)}^{2}}}}} + {{{{3}} {{{\phi_L}}} \cdot {{{{\phi_R}}^{2}}} {{{cos\left( {\theta_L}\right)}^{2}}} {{{sin\left( {\theta_L}\right)}^{2}}}} - {{{3}} {{{\phi_L}}} \cdot {{{{\phi_R}}^{2}}} {{{sin\left( {\theta_L}\right)}^{2}}}}} + {{{6}} {{{\phi_L}}} \cdot {{{{\phi_R}}^{2}}}} + {{{{{6}} {{{\phi_L}}} \cdot {{{cos\left( {\theta_L}\right)}^{2}}}} - {{{6}} {{{\phi_L}}}}} - {{{3}} {{{\phi_R}}} \cdot {{{{\phi_L}}^{2}}} {{{cos\left( {\theta_L}\right)}^{4}}}}} + {{{{9}} {{{\phi_R}}} \cdot {{{{\phi_L}}^{2}}} {{{cos\left( {\theta_L}\right)}^{2}}}} - {{{3}} {{{\phi_R}}} \cdot {{{{\phi_L}}^{2}}} {{{cos\left( {\theta_L}\right)}^{2}}} {{{sin\left( {\theta_L}\right)}^{2}}}}} + {{{{{3}} {{{\phi_R}}} \cdot {{{{\phi_L}}^{2}}} {{{sin\left( {\theta_L}\right)}^{2}}}} - {{{6}} {{{\phi_R}}} \cdot {{{{\phi_L}}^{2}}}}} - {{{6}} {{{\phi_R}}} \cdot {{{cos\left( {\theta_L}\right)}^{2}}}}} + {{{6}} {{{\phi_R}}}} + {{{{{\phi_L}}^{3}}} {{{cos\left( {\theta_L}\right)}^{2}}} {{{sin\left( {\theta_L}\right)}^{2}}}} + {{{{{{{\phi_L}}^{3}}} {{{cos\left( {\theta_L}\right)}^{4}}}} - {{{3}} {{{{\phi_L}}^{3}}} {{{cos\left( {\theta_L}\right)}^{2}}}}} - {{{{{\phi_L}}^{3}}} {{{sin\left( {\theta_L}\right)}^{2}}}}} + {{{2}} {{{{\phi_L}}^{3}}}} + {{{{{3}} {{{{\phi_R}}^{3}}} {{{cos\left( {\theta_L}\right)}^{2}}}} - {{{{{\phi_R}}^{3}}} {{{cos\left( {\theta_L}\right)}^{4}}}}} - {{{{{\phi_R}}^{3}}} {{{sin\left( {\theta_L}\right)}^{2}}} {{{cos\left( {\theta_L}\right)}^{2}}}}} + {{{{{{\phi_R}}^{3}}} {{{sin\left( {\theta_L}\right)}^{2}}}} - {{{2}} {{{{\phi_R}}^{3}}}}}})}}}{{{6}} {{cosh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)}}} \\ \frac{-{{{{({{{\phi_L}} - {{\phi_R}}})}^{2}}} {{sin\left( {\theta_L}\right)}} {{cos\left( {\theta_L}\right)}} {{cosh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)}}}}{{{2}} {{w}} {{sinh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)}}} & {\frac{1}{2}}{({{{{cos\left( {\theta_L}\right)}^{2}}} {{({{{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_L}}^{2}}} - {{{\phi_R}}^{2}}})}}})} & {\frac{1}{6}}{({{{sin\left( {\theta_L}\right)}} {{cos\left( {\theta_L}\right)}} {{({{{{{{3}} {{{\phi_L}}} \cdot {{{{\phi_R}}^{2}}}} - {{{6}} {{{\phi_L}}}}} - {{{3}} {{{\phi_R}}} \cdot {{{{\phi_L}}^{2}}}}} + {{{{6}} {{{\phi_R}}}} - {{{\phi_R}}^{3}}} + {{{\phi_L}}^{3}}})}}})} \\ \frac{-{{{cosh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)}} {{({{{{3}} {{{\phi_L}}} \cdot {{{{\phi_R}}^{2}}}} + {{{{{\phi_L}}^{3}} - {{{6}} {{{\phi_L}}}}} - {{{3}} {{{\phi_R}}} \cdot {{{{\phi_L}}^{2}}}}} + {{{{6}} {{{\phi_R}}}} - {{{\phi_R}}^{3}}}})}}}}{{{6}} {{w}} {{sinh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)}}} & \frac{-{{{cos\left( {\theta_L}\right)}} {{({{{{3}} {{{\phi_L}}} \cdot {{{{\phi_R}}^{2}}}} + {{{{{\phi_L}}^{3}} - {{{6}} {{{\phi_L}}}}} - {{{3}} {{{\phi_R}}} \cdot {{{{\phi_L}}^{2}}}}} + {{{{6}} {{{\phi_R}}}} - {{{\phi_R}}^{3}}}})}}}}{{{6}} {{sin\left( {\theta_L}\right)}}} & {\frac{1}{2}}{({-{({{{{{\phi_L}}^{2}} - {{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}}} + {{{\phi_R}}^{2}}})}})}\end{matrix}\right]} + {{\mathcal{O}(A^4)}}})}} {\left[\begin{matrix} \frac{cosh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}{cosh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)} & 0 & 0 \\ 0 & \frac{|{sinh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}|}{|{sinh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)}|} & 0 \\ 0 & 0 & \frac{|{sinh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}|}{|{sinh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)}|}\end{matrix}\right]}}$ = $\left[\begin{matrix} \left[\begin{matrix} 0 & \frac{{{w}} {{cos\left( {\theta_L}\right)}} {{sin\left( {\theta_L}\right)}} {{({{{{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}} \cdot {{cosh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)}} {{sinh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}}} - {{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}} \cdot {{cosh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}} {{sinh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)}}}} - {{{{{\phi_L}}^{2}}} {{sinh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}} {{cosh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)}}}} + {{{{{{\phi_L}}^{2}}} {{cosh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}} {{sinh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)}}} - {{{{{\phi_R}}^{2}}} {{sinh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}} {{cosh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)}}}} + {{{{{\phi_R}}^{2}}} {{cosh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}} {{sinh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)}}}})}}}{{{2}} {{{cosh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)}^{2}}}} & \frac{{{w}} {{({{{{{9}} {{{\phi_L}}} \cdot {{{{\phi_R}}^{2}}} {{{cos\left( {\theta_L}\right)}^{2}}} {{sinh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)}} {{cosh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}}} - {{{9}} {{{\phi_L}}} \cdot {{{{\phi_R}}^{2}}} {{{cos\left( {\theta_L}\right)}^{2}}} {{sinh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}} {{cosh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)}}}} + {{{{3}} {{{\phi_L}}} \cdot {{{{\phi_R}}^{2}}} {{{cos\left( {\theta_L}\right)}^{2}}} {{{sin\left( {\theta_L}\right)}^{2}}} {{cosh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)}} {{sinh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}}} - {{{3}} {{{\phi_L}}} \cdot {{{{\phi_R}}^{2}}} {{{cos\left( {\theta_L}\right)}^{2}}} {{{sin\left( {\theta_L}\right)}^{2}}} {{cosh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}} {{sinh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)}}}} + {{{{3}} {{{\phi_L}}} \cdot {{{{\phi_R}}^{2}}} {{{cos\left( {\theta_L}\right)}^{4}}} {{sinh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}} {{cosh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)}}} - {{{3}} {{{\phi_L}}} \cdot {{{{\phi_R}}^{2}}} {{{cos\left( {\theta_L}\right)}^{4}}} {{sinh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)}} {{cosh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}}}} + {{{{3}} {{{\phi_L}}} \cdot {{{{\phi_R}}^{2}}} {{{sin\left( {\theta_L}\right)}^{2}}} {{sinh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)}} {{cosh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}}} - {{{3}} {{{\phi_L}}} \cdot {{{{\phi_R}}^{2}}} {{{sin\left( {\theta_L}\right)}^{2}}} {{sinh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}} {{cosh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)}}}} + {{{{{6}} {{{\phi_L}}} \cdot {{{{\phi_R}}^{2}}} {{cosh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)}} {{sinh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}}} - {{{6}} {{{\phi_L}}} \cdot {{{{\phi_R}}^{2}}} {{cosh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}} {{sinh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)}}}} - {{{6}} {{{\phi_L}}} \cdot {{{cos\left( {\theta_L}\right)}^{2}}} {{cosh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}} {{sinh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)}}}} + {{{{6}} {{{\phi_L}}} \cdot {{{cos\left( {\theta_L}\right)}^{2}}} {{cosh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)}} {{sinh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}}} - {{{6}} {{{\phi_L}}} \cdot {{sinh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}} {{cosh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)}}}} + {{{{6}} {{{\phi_L}}} \cdot {{sinh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)}} {{cosh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}}} - {{{9}} {{{\phi_R}}} \cdot {{{{\phi_L}}^{2}}} {{{cos\left( {\theta_L}\right)}^{2}}} {{sinh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)}} {{cosh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}}}} + {{{{9}} {{{\phi_R}}} \cdot {{{{\phi_L}}^{2}}} {{{cos\left( {\theta_L}\right)}^{2}}} {{sinh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}} {{cosh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)}}} - {{{3}} {{{\phi_R}}} \cdot {{{{\phi_L}}^{2}}} {{{cos\left( {\theta_L}\right)}^{2}}} {{{sin\left( {\theta_L}\right)}^{2}}} {{cosh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)}} {{sinh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}}}} + {{{{3}} {{{\phi_R}}} \cdot {{{{\phi_L}}^{2}}} {{{cos\left( {\theta_L}\right)}^{2}}} {{{sin\left( {\theta_L}\right)}^{2}}} {{cosh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}} {{sinh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)}}} - {{{3}} {{{\phi_R}}} \cdot {{{{\phi_L}}^{2}}} {{{cos\left( {\theta_L}\right)}^{4}}} {{sinh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}} {{cosh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)}}}} + {{{{3}} {{{\phi_R}}} \cdot {{{{\phi_L}}^{2}}} {{{cos\left( {\theta_L}\right)}^{4}}} {{sinh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)}} {{cosh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}}} - {{{3}} {{{\phi_R}}} \cdot {{{{\phi_L}}^{2}}} {{{sin\left( {\theta_L}\right)}^{2}}} {{sinh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)}} {{cosh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}}}} + {{{{3}} {{{\phi_R}}} \cdot {{{{\phi_L}}^{2}}} {{{sin\left( {\theta_L}\right)}^{2}}} {{sinh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}} {{cosh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)}}} - {{{6}} {{{\phi_R}}} \cdot {{{{\phi_L}}^{2}}} {{cosh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)}} {{sinh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}}}} + {{{6}} {{{\phi_R}}} \cdot {{{{\phi_L}}^{2}}} {{cosh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}} {{sinh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)}}} + {{{{6}} {{{\phi_R}}} \cdot {{{cos\left( {\theta_L}\right)}^{2}}} {{cosh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}} {{sinh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)}}} - {{{6}} {{{\phi_R}}} \cdot {{{cos\left( {\theta_L}\right)}^{2}}} {{cosh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)}} {{sinh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}}}} + {{{{{6}} {{{\phi_R}}} \cdot {{sinh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}} {{cosh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)}}} - {{{6}} {{{\phi_R}}} \cdot {{sinh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)}} {{cosh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}}}} - {{{{{\phi_L}}^{3}}} {{{cos\left( {\theta_L}\right)}^{4}}} {{cosh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}} {{sinh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)}}}} + {{{{{3}} {{{{\phi_L}}^{3}}} {{{cos\left( {\theta_L}\right)}^{2}}} {{cosh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}} {{sinh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)}}} - {{{3}} {{{{\phi_L}}^{3}}} {{{cos\left( {\theta_L}\right)}^{2}}} {{cosh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)}} {{sinh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}}}} - {{{{{\phi_L}}^{3}}} {{{sin\left( {\theta_L}\right)}^{2}}} {{{cos\left( {\theta_L}\right)}^{2}}} {{sinh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)}} {{cosh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}}}} + {{{{{{\phi_L}}^{3}}} {{{cos\left( {\theta_L}\right)}^{4}}} {{sinh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}} {{cosh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)}}} - {{{2}} {{{{\phi_L}}^{3}}} {{sinh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)}} {{cosh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}}}} + {{{{{\phi_L}}^{3}}} {{{cos\left( {\theta_L}\right)}^{2}}} {{{sin\left( {\theta_L}\right)}^{2}}} {{cosh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)}} {{sinh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}}} + {{{{{{\phi_L}}^{3}}} {{{sin\left( {\theta_L}\right)}^{2}}} {{sinh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)}} {{cosh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}}} - {{{{{\phi_L}}^{3}}} {{{sin\left( {\theta_L}\right)}^{2}}} {{cosh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)}} {{sinh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}}}} + {{{{2}} {{{{\phi_L}}^{3}}} {{sinh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}} {{cosh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)}}} - {{{3}} {{{{\phi_R}}^{3}}} {{{cos\left( {\theta_L}\right)}^{2}}} {{cosh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}} {{sinh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)}}}} + {{{{{3}} {{{{\phi_R}}^{3}}} {{{cos\left( {\theta_L}\right)}^{2}}} {{cosh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)}} {{sinh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}}} - {{{{{\phi_R}}^{3}}} {{{cos\left( {\theta_L}\right)}^{4}}} {{cosh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)}} {{sinh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}}}} - {{{{{\phi_R}}^{3}}} {{{sin\left( {\theta_L}\right)}^{2}}} {{{cos\left( {\theta_L}\right)}^{2}}} {{sinh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}} {{cosh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)}}}} + {{{{{\phi_R}}^{3}}} {{{cos\left( {\theta_L}\right)}^{4}}} {{sinh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)}} {{cosh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}}} + {{{{{{\phi_R}}^{3}}} {{{cos\left( {\theta_L}\right)}^{2}}} {{{sin\left( {\theta_L}\right)}^{2}}} {{cosh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}} {{sinh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)}}} - {{{{{\phi_R}}^{3}}} {{{sin\left( {\theta_L}\right)}^{2}}} {{cosh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}} {{sinh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)}}}} + {{{{{{\phi_R}}^{3}}} {{{sin\left( {\theta_L}\right)}^{2}}} {{sinh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}} {{cosh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)}}} - {{{2}} {{{{\phi_R}}^{3}}} {{sinh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}} {{cosh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)}}}} + {{{2}} {{{{\phi_R}}^{3}}} {{sinh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)}} {{cosh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}}}})}}}{{{6}} {{{cosh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)}^{2}}}} \\ \frac{-{{{({{{{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}} \cdot {{cosh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)}} {{sinh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}}} - {{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}} \cdot {{cosh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}} {{sinh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)}}}} - {{{{{\phi_L}}^{2}}} {{sinh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}} {{cosh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)}}}} + {{{{{{\phi_L}}^{2}}} {{cosh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}} {{sinh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)}}} - {{{{{\phi_R}}^{2}}} {{sinh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}} {{cosh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)}}}} + {{{{{\phi_R}}^{2}}} {{cosh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}} {{sinh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)}}}})}} {{cosh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}} {{sin\left( {\theta_L}\right)}} {{cos\left( {\theta_L}\right)}}}}{{{2}} {{w}} {{sinh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)}} {{sinh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}} {{cosh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)}}} & 0 & 0 \\ \frac{-{{{cosh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}} {{({{{{{3}} {{{\phi_L}}} \cdot {{{{\phi_R}}^{2}}} {{cosh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}} {{sinh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)}}} - {{{3}} {{{\phi_L}}} \cdot {{{{\phi_R}}^{2}}} {{cosh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)}} {{sinh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}}}} + {{{{6}} {{{\phi_L}}} \cdot {{sinh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}} {{cosh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)}}} - {{{6}} {{{\phi_L}}} \cdot {{sinh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)}} {{cosh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}}}} + {{{{{{{\phi_L}}^{3}}} {{cosh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}} {{sinh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)}}} - {{{{{\phi_L}}^{3}}} {{sinh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}} {{cosh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)}}}} - {{{3}} {{{\phi_R}}} \cdot {{{{\phi_L}}^{2}}} {{cosh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}} {{sinh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)}}}} + {{{3}} {{{\phi_R}}} \cdot {{{{\phi_L}}^{2}}} {{cosh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)}} {{sinh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}}} + {{{{{{\phi_R}}^{3}}} {{cosh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)}} {{sinh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}}} - {{{6}} {{{\phi_R}}} \cdot {{sinh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}} {{cosh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)}}}} + {{{{6}} {{{\phi_R}}} \cdot {{sinh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)}} {{cosh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}}} - {{{{{\phi_R}}^{3}}} {{sinh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)}} {{cosh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}}}}})}}}}{{{6}} {{w}} {{sinh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)}} {{sinh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}} {{cosh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)}}} & 0 & 0\end{matrix}\right] & 0 & 0 \\ 0 & \left[\begin{matrix} 0 & \frac{-{{{w}} {{sin\left( {\theta_L}\right)}} {{|{sinh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}|}} {{({{{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}} \cdot {{cosh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}} {{sinh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)}}} - {{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}} \cdot {{cosh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)}} {{sinh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}}}} + {{{{{{\phi_L}}^{2}}} {{cosh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)}} {{sinh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}}} - {{{{{\phi_L}}^{2}}} {{sinh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)}} {{cosh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}}}} + {{{{{{\phi_R}}^{2}}} {{cosh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)}} {{sinh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}}} - {{{{{\phi_R}}^{2}}} {{sinh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)}} {{cosh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}}}}})}} {{cos\left( {\theta_L}\right)}}}}{{{2}} {{cosh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}} {{cosh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)}} {{|{sinh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)}|}}} & \frac{-{{{w}} {{|{sinh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}|}} {{({{{{{{6}} {{{\phi_L}}} \cdot {{{{\phi_R}}^{2}}} {{cosh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}} {{sinh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)}}} - {{{6}} {{{\phi_L}}} \cdot {{{{\phi_R}}^{2}}} {{cosh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)}} {{sinh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}}}} - {{{9}} {{{\phi_L}}} \cdot {{{{\phi_R}}^{2}}} {{{cos\left( {\theta_L}\right)}^{2}}} {{sinh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)}} {{cosh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}}}} + {{{{9}} {{{\phi_L}}} \cdot {{{{\phi_R}}^{2}}} {{{cos\left( {\theta_L}\right)}^{2}}} {{sinh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}} {{cosh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)}}} - {{{3}} {{{\phi_L}}} \cdot {{{{\phi_R}}^{2}}} {{{cos\left( {\theta_L}\right)}^{4}}} {{sinh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}} {{cosh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)}}}} + {{{{3}} {{{\phi_L}}} \cdot {{{{\phi_R}}^{2}}} {{{cos\left( {\theta_L}\right)}^{4}}} {{sinh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)}} {{cosh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}}} - {{{3}} {{{\phi_L}}} \cdot {{{{\phi_R}}^{2}}} {{{sin\left( {\theta_L}\right)}^{2}}} {{sinh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)}} {{cosh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}}}} + {{{{3}} {{{\phi_L}}} \cdot {{{{\phi_R}}^{2}}} {{{sin\left( {\theta_L}\right)}^{2}}} {{sinh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}} {{cosh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)}}} - {{{3}} {{{\phi_L}}} \cdot {{{{\phi_R}}^{2}}} {{{cos\left( {\theta_L}\right)}^{2}}} {{{sin\left( {\theta_L}\right)}^{2}}} {{cosh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)}} {{sinh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}}}} + {{{3}} {{{\phi_L}}} \cdot {{{{\phi_R}}^{2}}} {{{cos\left( {\theta_L}\right)}^{2}}} {{{sin\left( {\theta_L}\right)}^{2}}} {{cosh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}} {{sinh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)}}} + {{{{6}} {{{\phi_L}}} \cdot {{sinh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}} {{cosh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)}}} - {{{6}} {{{\phi_L}}} \cdot {{sinh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)}} {{cosh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}}}} + {{{{{6}} {{{\phi_L}}} \cdot {{{cos\left( {\theta_L}\right)}^{2}}} {{cosh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}} {{sinh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)}}} - {{{6}} {{{\phi_L}}} \cdot {{{cos\left( {\theta_L}\right)}^{2}}} {{cosh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)}} {{sinh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}}}} - {{{6}} {{{\phi_R}}} \cdot {{{{\phi_L}}^{2}}} {{cosh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}} {{sinh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)}}}} + {{{6}} {{{\phi_R}}} \cdot {{{{\phi_L}}^{2}}} {{cosh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)}} {{sinh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}}} + {{{{9}} {{{\phi_R}}} \cdot {{{{\phi_L}}^{2}}} {{{cos\left( {\theta_L}\right)}^{2}}} {{sinh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)}} {{cosh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}}} - {{{9}} {{{\phi_R}}} \cdot {{{{\phi_L}}^{2}}} {{{cos\left( {\theta_L}\right)}^{2}}} {{sinh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}} {{cosh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)}}}} + {{{{3}} {{{\phi_R}}} \cdot {{{{\phi_L}}^{2}}} {{{cos\left( {\theta_L}\right)}^{4}}} {{sinh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}} {{cosh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)}}} - {{{3}} {{{\phi_R}}} \cdot {{{{\phi_L}}^{2}}} {{{cos\left( {\theta_L}\right)}^{4}}} {{sinh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)}} {{cosh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}}}} + {{{{3}} {{{\phi_R}}} \cdot {{{{\phi_L}}^{2}}} {{{sin\left( {\theta_L}\right)}^{2}}} {{sinh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)}} {{cosh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}}} - {{{3}} {{{\phi_R}}} \cdot {{{{\phi_L}}^{2}}} {{{sin\left( {\theta_L}\right)}^{2}}} {{sinh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}} {{cosh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)}}}} + {{{{{3}} {{{\phi_R}}} \cdot {{{{\phi_L}}^{2}}} {{{cos\left( {\theta_L}\right)}^{2}}} {{{sin\left( {\theta_L}\right)}^{2}}} {{cosh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)}} {{sinh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}}} - {{{3}} {{{\phi_R}}} \cdot {{{{\phi_L}}^{2}}} {{{cos\left( {\theta_L}\right)}^{2}}} {{{sin\left( {\theta_L}\right)}^{2}}} {{cosh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}} {{sinh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)}}}} - {{{6}} {{{\phi_R}}} \cdot {{sinh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}} {{cosh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)}}}} + {{{{6}} {{{\phi_R}}} \cdot {{sinh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)}} {{cosh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}}} - {{{6}} {{{\phi_R}}} \cdot {{{cos\left( {\theta_L}\right)}^{2}}} {{cosh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}} {{sinh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)}}}} + {{{{6}} {{{\phi_R}}} \cdot {{{cos\left( {\theta_L}\right)}^{2}}} {{cosh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)}} {{sinh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}}} - {{{2}} {{{{\phi_L}}^{3}}} {{sinh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}} {{cosh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)}}}} + {{{2}} {{{{\phi_L}}^{3}}} {{sinh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)}} {{cosh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}}} + {{{{{{\phi_L}}^{3}}} {{{cos\left( {\theta_L}\right)}^{4}}} {{sinh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)}} {{cosh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}}} - {{{3}} {{{{\phi_L}}^{3}}} {{{cos\left( {\theta_L}\right)}^{2}}} {{cosh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}} {{sinh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)}}}} + {{{{{{3}} {{{{\phi_L}}^{3}}} {{{cos\left( {\theta_L}\right)}^{2}}} {{cosh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)}} {{sinh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}}} - {{{{{\phi_L}}^{3}}} {{{cos\left( {\theta_L}\right)}^{4}}} {{cosh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)}} {{sinh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}}}} - {{{{{\phi_L}}^{3}}} {{{sin\left( {\theta_L}\right)}^{2}}} {{{cos\left( {\theta_L}\right)}^{2}}} {{sinh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}} {{cosh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)}}}} - {{{{{\phi_L}}^{3}}} {{{sin\left( {\theta_L}\right)}^{2}}} {{cosh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}} {{sinh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)}}}} + {{{{{\phi_L}}^{3}}} {{{sin\left( {\theta_L}\right)}^{2}}} {{sinh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}} {{cosh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)}}} + {{{{{{{\phi_L}}^{3}}} {{{cos\left( {\theta_L}\right)}^{2}}} {{{sin\left( {\theta_L}\right)}^{2}}} {{cosh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}} {{sinh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)}}} - {{{2}} {{{{\phi_R}}^{3}}} {{sinh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)}} {{cosh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}}}} - {{{3}} {{{{\phi_R}}^{3}}} {{{cos\left( {\theta_L}\right)}^{2}}} {{cosh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)}} {{sinh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}}}} + {{{{{{{\phi_R}}^{3}}} {{{cos\left( {\theta_L}\right)}^{4}}} {{sinh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}} {{cosh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)}}} - {{{{{\phi_R}}^{3}}} {{{cos\left( {\theta_L}\right)}^{4}}} {{cosh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}} {{sinh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)}}}} - {{{{{\phi_R}}^{3}}} {{{sin\left( {\theta_L}\right)}^{2}}} {{{cos\left( {\theta_L}\right)}^{2}}} {{sinh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)}} {{cosh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}}}} + {{{3}} {{{{\phi_R}}^{3}}} {{{cos\left( {\theta_L}\right)}^{2}}} {{cosh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}} {{sinh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)}}} + {{{{{{\phi_R}}^{3}}} {{{sin\left( {\theta_L}\right)}^{2}}} {{sinh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)}} {{cosh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}}} - {{{{{\phi_R}}^{3}}} {{{sin\left( {\theta_L}\right)}^{2}}} {{cosh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)}} {{sinh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}}}} + {{{{{\phi_R}}^{3}}} {{{cos\left( {\theta_L}\right)}^{2}}} {{{sin\left( {\theta_L}\right)}^{2}}} {{cosh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)}} {{sinh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}}} + {{{2}} {{{{\phi_R}}^{3}}} {{sinh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}} {{cosh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)}}}})}}}}{{{6}} {{cosh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}} {{cosh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)}} {{|{sinh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)}|}}} \\ \frac{-{{{({{{{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}} \cdot {{cosh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)}} {{sinh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}}} - {{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}} \cdot {{cosh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}} {{sinh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)}}}} - {{{{{\phi_L}}^{2}}} {{sinh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}} {{cosh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)}}}} + {{{{{{\phi_L}}^{2}}} {{cosh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}} {{sinh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)}}} - {{{{{\phi_R}}^{2}}} {{sinh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}} {{cosh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)}}}} + {{{{{\phi_R}}^{2}}} {{cosh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}} {{sinh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)}}}})}} {{|{sinh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}|}} {{cos\left( {\theta_L}\right)}} {{sin\left( {\theta_L}\right)}}}}{{{2}} {{w}} {{sinh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)}} {{sinh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}} {{|{sinh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)}|}}} & 0 & 0 \\ \frac{-{{{|{sinh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}|}} {{({{{{{3}} {{{\phi_L}}} \cdot {{{{\phi_R}}^{2}}} {{cosh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}} {{sinh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)}}} - {{{3}} {{{\phi_L}}} \cdot {{{{\phi_R}}^{2}}} {{cosh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)}} {{sinh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}}}} + {{{{6}} {{{\phi_L}}} \cdot {{sinh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}} {{cosh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)}}} - {{{6}} {{{\phi_L}}} \cdot {{sinh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)}} {{cosh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}}}} + {{{{{{{\phi_L}}^{3}}} {{cosh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}} {{sinh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)}}} - {{{{{\phi_L}}^{3}}} {{sinh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}} {{cosh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)}}}} - {{{3}} {{{\phi_R}}} \cdot {{{{\phi_L}}^{2}}} {{cosh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}} {{sinh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)}}}} + {{{3}} {{{\phi_R}}} \cdot {{{{\phi_L}}^{2}}} {{cosh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)}} {{sinh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}}} + {{{{{{\phi_R}}^{3}}} {{cosh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)}} {{sinh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}}} - {{{6}} {{{\phi_R}}} \cdot {{sinh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}} {{cosh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)}}}} + {{{{6}} {{{\phi_R}}} \cdot {{sinh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)}} {{cosh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}}} - {{{{{\phi_R}}^{3}}} {{sinh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)}} {{cosh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}}}}})}}}}{{{6}} {{w}} {{sinh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)}} {{sinh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}} {{|{sinh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)}|}}} & 0 & 0\end{matrix}\right] & 0 \\ 0 & 0 & \left[\begin{matrix} 0 & \frac{-{{{w}} {{sin\left( {\theta_L}\right)}} {{|{sinh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}|}} {{({{{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}} \cdot {{cosh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}} {{sinh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)}}} - {{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}} \cdot {{cosh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)}} {{sinh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}}}} + {{{{{{\phi_L}}^{2}}} {{cosh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)}} {{sinh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}}} - {{{{{\phi_L}}^{2}}} {{sinh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)}} {{cosh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}}}} + {{{{{{\phi_R}}^{2}}} {{cosh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)}} {{sinh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}}} - {{{{{\phi_R}}^{2}}} {{sinh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)}} {{cosh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}}}}})}} {{cos\left( {\theta_L}\right)}}}}{{{2}} {{cosh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}} {{cosh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)}} {{|{sinh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)}|}}} & \frac{-{{{w}} {{|{sinh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}|}} {{({{{{{{6}} {{{\phi_L}}} \cdot {{{{\phi_R}}^{2}}} {{cosh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}} {{sinh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)}}} - {{{6}} {{{\phi_L}}} \cdot {{{{\phi_R}}^{2}}} {{cosh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)}} {{sinh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}}}} - {{{9}} {{{\phi_L}}} \cdot {{{{\phi_R}}^{2}}} {{{cos\left( {\theta_L}\right)}^{2}}} {{sinh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)}} {{cosh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}}}} + {{{{9}} {{{\phi_L}}} \cdot {{{{\phi_R}}^{2}}} {{{cos\left( {\theta_L}\right)}^{2}}} {{sinh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}} {{cosh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)}}} - {{{3}} {{{\phi_L}}} \cdot {{{{\phi_R}}^{2}}} {{{cos\left( {\theta_L}\right)}^{4}}} {{sinh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}} {{cosh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)}}}} + {{{{3}} {{{\phi_L}}} \cdot {{{{\phi_R}}^{2}}} {{{cos\left( {\theta_L}\right)}^{4}}} {{sinh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)}} {{cosh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}}} - {{{3}} {{{\phi_L}}} \cdot {{{{\phi_R}}^{2}}} {{{sin\left( {\theta_L}\right)}^{2}}} {{sinh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)}} {{cosh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}}}} + {{{{3}} {{{\phi_L}}} \cdot {{{{\phi_R}}^{2}}} {{{sin\left( {\theta_L}\right)}^{2}}} {{sinh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}} {{cosh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)}}} - {{{3}} {{{\phi_L}}} \cdot {{{{\phi_R}}^{2}}} {{{cos\left( {\theta_L}\right)}^{2}}} {{{sin\left( {\theta_L}\right)}^{2}}} {{cosh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)}} {{sinh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}}}} + {{{3}} {{{\phi_L}}} \cdot {{{{\phi_R}}^{2}}} {{{cos\left( {\theta_L}\right)}^{2}}} {{{sin\left( {\theta_L}\right)}^{2}}} {{cosh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}} {{sinh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)}}} + {{{{6}} {{{\phi_L}}} \cdot {{sinh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}} {{cosh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)}}} - {{{6}} {{{\phi_L}}} \cdot {{sinh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)}} {{cosh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}}}} + {{{{{6}} {{{\phi_L}}} \cdot {{{cos\left( {\theta_L}\right)}^{2}}} {{cosh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}} {{sinh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)}}} - {{{6}} {{{\phi_L}}} \cdot {{{cos\left( {\theta_L}\right)}^{2}}} {{cosh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)}} {{sinh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}}}} - {{{6}} {{{\phi_R}}} \cdot {{{{\phi_L}}^{2}}} {{cosh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}} {{sinh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)}}}} + {{{6}} {{{\phi_R}}} \cdot {{{{\phi_L}}^{2}}} {{cosh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)}} {{sinh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}}} + {{{{9}} {{{\phi_R}}} \cdot {{{{\phi_L}}^{2}}} {{{cos\left( {\theta_L}\right)}^{2}}} {{sinh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)}} {{cosh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}}} - {{{9}} {{{\phi_R}}} \cdot {{{{\phi_L}}^{2}}} {{{cos\left( {\theta_L}\right)}^{2}}} {{sinh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}} {{cosh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)}}}} + {{{{3}} {{{\phi_R}}} \cdot {{{{\phi_L}}^{2}}} {{{cos\left( {\theta_L}\right)}^{4}}} {{sinh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}} {{cosh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)}}} - {{{3}} {{{\phi_R}}} \cdot {{{{\phi_L}}^{2}}} {{{cos\left( {\theta_L}\right)}^{4}}} {{sinh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)}} {{cosh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}}}} + {{{{3}} {{{\phi_R}}} \cdot {{{{\phi_L}}^{2}}} {{{sin\left( {\theta_L}\right)}^{2}}} {{sinh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)}} {{cosh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}}} - {{{3}} {{{\phi_R}}} \cdot {{{{\phi_L}}^{2}}} {{{sin\left( {\theta_L}\right)}^{2}}} {{sinh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}} {{cosh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)}}}} + {{{{{3}} {{{\phi_R}}} \cdot {{{{\phi_L}}^{2}}} {{{cos\left( {\theta_L}\right)}^{2}}} {{{sin\left( {\theta_L}\right)}^{2}}} {{cosh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)}} {{sinh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}}} - {{{3}} {{{\phi_R}}} \cdot {{{{\phi_L}}^{2}}} {{{cos\left( {\theta_L}\right)}^{2}}} {{{sin\left( {\theta_L}\right)}^{2}}} {{cosh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}} {{sinh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)}}}} - {{{6}} {{{\phi_R}}} \cdot {{sinh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}} {{cosh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)}}}} + {{{{6}} {{{\phi_R}}} \cdot {{sinh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)}} {{cosh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}}} - {{{6}} {{{\phi_R}}} \cdot {{{cos\left( {\theta_L}\right)}^{2}}} {{cosh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}} {{sinh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)}}}} + {{{{6}} {{{\phi_R}}} \cdot {{{cos\left( {\theta_L}\right)}^{2}}} {{cosh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)}} {{sinh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}}} - {{{2}} {{{{\phi_L}}^{3}}} {{sinh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}} {{cosh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)}}}} + {{{2}} {{{{\phi_L}}^{3}}} {{sinh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)}} {{cosh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}}} + {{{{{{\phi_L}}^{3}}} {{{cos\left( {\theta_L}\right)}^{4}}} {{sinh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)}} {{cosh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}}} - {{{3}} {{{{\phi_L}}^{3}}} {{{cos\left( {\theta_L}\right)}^{2}}} {{cosh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}} {{sinh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)}}}} + {{{{{{3}} {{{{\phi_L}}^{3}}} {{{cos\left( {\theta_L}\right)}^{2}}} {{cosh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)}} {{sinh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}}} - {{{{{\phi_L}}^{3}}} {{{cos\left( {\theta_L}\right)}^{4}}} {{cosh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)}} {{sinh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}}}} - {{{{{\phi_L}}^{3}}} {{{sin\left( {\theta_L}\right)}^{2}}} {{{cos\left( {\theta_L}\right)}^{2}}} {{sinh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}} {{cosh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)}}}} - {{{{{\phi_L}}^{3}}} {{{sin\left( {\theta_L}\right)}^{2}}} {{cosh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}} {{sinh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)}}}} + {{{{{\phi_L}}^{3}}} {{{sin\left( {\theta_L}\right)}^{2}}} {{sinh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}} {{cosh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)}}} + {{{{{{{\phi_L}}^{3}}} {{{cos\left( {\theta_L}\right)}^{2}}} {{{sin\left( {\theta_L}\right)}^{2}}} {{cosh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}} {{sinh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)}}} - {{{2}} {{{{\phi_R}}^{3}}} {{sinh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)}} {{cosh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}}}} - {{{3}} {{{{\phi_R}}^{3}}} {{{cos\left( {\theta_L}\right)}^{2}}} {{cosh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)}} {{sinh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}}}} + {{{{{{{\phi_R}}^{3}}} {{{cos\left( {\theta_L}\right)}^{4}}} {{sinh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}} {{cosh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)}}} - {{{{{\phi_R}}^{3}}} {{{cos\left( {\theta_L}\right)}^{4}}} {{cosh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}} {{sinh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)}}}} - {{{{{\phi_R}}^{3}}} {{{sin\left( {\theta_L}\right)}^{2}}} {{{cos\left( {\theta_L}\right)}^{2}}} {{sinh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)}} {{cosh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}}}} + {{{3}} {{{{\phi_R}}^{3}}} {{{cos\left( {\theta_L}\right)}^{2}}} {{cosh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}} {{sinh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)}}} + {{{{{{\phi_R}}^{3}}} {{{sin\left( {\theta_L}\right)}^{2}}} {{sinh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)}} {{cosh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}}} - {{{{{\phi_R}}^{3}}} {{{sin\left( {\theta_L}\right)}^{2}}} {{cosh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)}} {{sinh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}}}} + {{{{{\phi_R}}^{3}}} {{{cos\left( {\theta_L}\right)}^{2}}} {{{sin\left( {\theta_L}\right)}^{2}}} {{cosh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)}} {{sinh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}}} + {{{2}} {{{{\phi_R}}^{3}}} {{sinh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}} {{cosh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)}}}})}}}}{{{6}} {{cosh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}} {{cosh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)}} {{|{sinh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)}|}}} \\ \frac{-{{{({{{{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}} \cdot {{cosh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)}} {{sinh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}}} - {{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}} \cdot {{cosh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}} {{sinh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)}}}} - {{{{{\phi_L}}^{2}}} {{sinh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}} {{cosh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)}}}} + {{{{{{\phi_L}}^{2}}} {{cosh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}} {{sinh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)}}} - {{{{{\phi_R}}^{2}}} {{sinh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}} {{cosh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)}}}} + {{{{{\phi_R}}^{2}}} {{cosh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}} {{sinh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)}}}})}} {{|{sinh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}|}} {{cos\left( {\theta_L}\right)}} {{sin\left( {\theta_L}\right)}}}}{{{2}} {{w}} {{sinh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)}} {{sinh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}} {{|{sinh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)}|}}} & 0 & 0 \\ \frac{-{{{|{sinh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}|}} {{({{{{{3}} {{{\phi_L}}} \cdot {{{{\phi_R}}^{2}}} {{cosh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}} {{sinh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)}}} - {{{3}} {{{\phi_L}}} \cdot {{{{\phi_R}}^{2}}} {{cosh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)}} {{sinh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}}}} + {{{{6}} {{{\phi_L}}} \cdot {{sinh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}} {{cosh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)}}} - {{{6}} {{{\phi_L}}} \cdot {{sinh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)}} {{cosh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}}}} + {{{{{{{\phi_L}}^{3}}} {{cosh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}} {{sinh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)}}} - {{{{{\phi_L}}^{3}}} {{sinh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}} {{cosh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)}}}} - {{{3}} {{{\phi_R}}} \cdot {{{{\phi_L}}^{2}}} {{cosh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}} {{sinh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)}}}} + {{{3}} {{{\phi_R}}} \cdot {{{{\phi_L}}^{2}}} {{cosh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)}} {{sinh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}}} + {{{{{{\phi_R}}^{3}}} {{cosh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)}} {{sinh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}}} - {{{6}} {{{\phi_R}}} \cdot {{sinh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}} {{cosh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)}}}} + {{{{6}} {{{\phi_R}}} \cdot {{sinh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)}} {{cosh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}}} - {{{{{\phi_R}}^{3}}} {{sinh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)}} {{cosh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}}}}})}}}}{{{6}} {{w}} {{sinh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)}} {{sinh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}} {{|{sinh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)}|}}} & 0 & 0\end{matrix}\right]\end{matrix}\right]$
[ ${ P}_{\theta}$ , ${ P}_{\phi}$ ] = ${ {\left[\begin{matrix} cos\left( {{{\theta_L}} - {{\theta_R}}}\right) & \frac{-{{{w}} {{sin\left( {{{\theta_L}} - {{\theta_R}}}\right)}} {{sinh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}}}}{cosh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)} & 0 \\ \frac{{{cosh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}} {{sin\left( {{{\theta_L}} - {{\theta_R}}}\right)}}}{{{w}} {{sinh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}}} & cos\left( {{{\theta_L}} - {{\theta_R}}}\right) & 0 \\ 0 & 0 & \frac{|{sin\left( {\theta_L}\right)}|}{|{sin\left( {\theta_R}\right)}|}\end{matrix}\right]} {{({{\left[\begin{matrix} {\frac{1}{2}}{({-{({{{{{\phi_L}}^{2}} - {{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}} \cdot {{{cos\left( {\theta_L}\right)}^{2}}}} - {{{{{\phi_L}}^{2}}} {{{cos\left( {\theta_L}\right)}^{2}}}}} + {{{{\phi_R}}^{2}} - {{{{{\phi_R}}^{2}}} {{{cos\left( {\theta_L}\right)}^{2}}}}}})}})} & \frac{{{w}} {{({{{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_L}}^{2}}} - {{{\phi_R}}^{2}}})}} {{sin\left( {\theta_L}\right)}} {{cos\left( {\theta_L}\right)}} {{sinh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}}}{{{2}} {{cosh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}}} & \frac{{{w}} {{sinh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}} {{({{{{{3}} {{{\phi_L}}} \cdot {{{{\phi_R}}^{2}}} {{{cos\left( {\theta_L}\right)}^{4}}}} - {{{9}} {{{\phi_L}}} \cdot {{{{\phi_R}}^{2}}} {{{cos\left( {\theta_L}\right)}^{2}}}}} + {{{{3}} {{{\phi_L}}} \cdot {{{{\phi_R}}^{2}}} {{{cos\left( {\theta_L}\right)}^{2}}} {{{sin\left( {\theta_L}\right)}^{2}}}} - {{{3}} {{{\phi_L}}} \cdot {{{{\phi_R}}^{2}}} {{{sin\left( {\theta_L}\right)}^{2}}}}} + {{{6}} {{{\phi_L}}} \cdot {{{{\phi_R}}^{2}}}} + {{{{{6}} {{{\phi_L}}} \cdot {{{cos\left( {\theta_L}\right)}^{2}}}} - {{{6}} {{{\phi_L}}}}} - {{{3}} {{{\phi_R}}} \cdot {{{{\phi_L}}^{2}}} {{{cos\left( {\theta_L}\right)}^{4}}}}} + {{{{9}} {{{\phi_R}}} \cdot {{{{\phi_L}}^{2}}} {{{cos\left( {\theta_L}\right)}^{2}}}} - {{{3}} {{{\phi_R}}} \cdot {{{{\phi_L}}^{2}}} {{{cos\left( {\theta_L}\right)}^{2}}} {{{sin\left( {\theta_L}\right)}^{2}}}}} + {{{{{3}} {{{\phi_R}}} \cdot {{{{\phi_L}}^{2}}} {{{sin\left( {\theta_L}\right)}^{2}}}} - {{{6}} {{{\phi_R}}} \cdot {{{{\phi_L}}^{2}}}}} - {{{6}} {{{\phi_R}}} \cdot {{{cos\left( {\theta_L}\right)}^{2}}}}} + {{{6}} {{{\phi_R}}}} + {{{{{\phi_L}}^{3}}} {{{cos\left( {\theta_L}\right)}^{2}}} {{{sin\left( {\theta_L}\right)}^{2}}}} + {{{{{{{\phi_L}}^{3}}} {{{cos\left( {\theta_L}\right)}^{4}}}} - {{{3}} {{{{\phi_L}}^{3}}} {{{cos\left( {\theta_L}\right)}^{2}}}}} - {{{{{\phi_L}}^{3}}} {{{sin\left( {\theta_L}\right)}^{2}}}}} + {{{2}} {{{{\phi_L}}^{3}}}} + {{{{{3}} {{{{\phi_R}}^{3}}} {{{cos\left( {\theta_L}\right)}^{2}}}} - {{{{{\phi_R}}^{3}}} {{{cos\left( {\theta_L}\right)}^{4}}}}} - {{{{{\phi_R}}^{3}}} {{{sin\left( {\theta_L}\right)}^{2}}} {{{cos\left( {\theta_L}\right)}^{2}}}}} + {{{{{{\phi_R}}^{3}}} {{{sin\left( {\theta_L}\right)}^{2}}}} - {{{2}} {{{{\phi_R}}^{3}}}}}})}}}{{{6}} {{cosh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}}} \\ \frac{-{{{{({{{\phi_L}} - {{\phi_R}}})}^{2}}} {{sin\left( {\theta_L}\right)}} {{cos\left( {\theta_L}\right)}} {{cosh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}}}}{{{2}} {{w}} {{sinh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}}} & {\frac{1}{2}}{({{{{cos\left( {\theta_L}\right)}^{2}}} {{({{{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_L}}^{2}}} - {{{\phi_R}}^{2}}})}}})} & {\frac{1}{6}}{({{{sin\left( {\theta_L}\right)}} {{cos\left( {\theta_L}\right)}} {{({{{{{{3}} {{{\phi_L}}} \cdot {{{{\phi_R}}^{2}}}} - {{{6}} {{{\phi_L}}}}} - {{{3}} {{{\phi_R}}} \cdot {{{{\phi_L}}^{2}}}}} + {{{{6}} {{{\phi_R}}}} - {{{\phi_R}}^{3}}} + {{{\phi_L}}^{3}}})}}})} \\ \frac{-{{{cosh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}} {{({{{{3}} {{{\phi_L}}} \cdot {{{{\phi_R}}^{2}}}} + {{{{{\phi_L}}^{3}} - {{{6}} {{{\phi_L}}}}} - {{{3}} {{{\phi_R}}} \cdot {{{{\phi_L}}^{2}}}}} + {{{{6}} {{{\phi_R}}}} - {{{\phi_R}}^{3}}}})}}}}{{{6}} {{w}} {{sinh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}}} & \frac{-{{{cos\left( {\theta_L}\right)}} {{({{{{3}} {{{\phi_L}}} \cdot {{{{\phi_R}}^{2}}}} + {{{{{\phi_L}}^{3}} - {{{6}} {{{\phi_L}}}}} - {{{3}} {{{\phi_R}}} \cdot {{{{\phi_L}}^{2}}}}} + {{{{6}} {{{\phi_R}}}} - {{{\phi_R}}^{3}}}})}}}}{{{6}} {{sin\left( {\theta_L}\right)}}} & {\frac{1}{2}}{({-{({{{{{\phi_L}}^{2}} - {{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}}} + {{{\phi_R}}^{2}}})}})}\end{matrix}\right]} + {{\mathcal{O}(A^4)}}})}}} - {{{({{\left[\begin{matrix} {\frac{1}{2}}{({-{({{{{{\phi_L}}^{2}} - {{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}} \cdot {{{cos\left( {\theta_R}\right)}^{2}}}} - {{{{{\phi_L}}^{2}}} {{{cos\left( {\theta_R}\right)}^{2}}}}} + {{{{\phi_R}}^{2}} - {{{{{\phi_R}}^{2}}} {{{cos\left( {\theta_R}\right)}^{2}}}}}})}})} & \frac{{{w}} {{({{{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_L}}^{2}}} - {{{\phi_R}}^{2}}})}} {{sin\left( {\theta_R}\right)}} {{cos\left( {\theta_R}\right)}} {{sinh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}}}{{{2}} {{cosh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}}} & \frac{{{w}} {{sinh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}} {{({{{{{3}} {{{\phi_L}}} \cdot {{{{\phi_R}}^{2}}} {{{cos\left( {\theta_R}\right)}^{4}}}} - {{{9}} {{{\phi_L}}} \cdot {{{{\phi_R}}^{2}}} {{{cos\left( {\theta_R}\right)}^{2}}}}} + {{{{3}} {{{\phi_L}}} \cdot {{{{\phi_R}}^{2}}} {{{cos\left( {\theta_R}\right)}^{2}}} {{{sin\left( {\theta_R}\right)}^{2}}}} - {{{3}} {{{\phi_L}}} \cdot {{{{\phi_R}}^{2}}} {{{sin\left( {\theta_R}\right)}^{2}}}}} + {{{6}} {{{\phi_L}}} \cdot {{{{\phi_R}}^{2}}}} + {{{{{6}} {{{\phi_L}}} \cdot {{{cos\left( {\theta_R}\right)}^{2}}}} - {{{6}} {{{\phi_L}}}}} - {{{3}} {{{\phi_R}}} \cdot {{{{\phi_L}}^{2}}} {{{cos\left( {\theta_R}\right)}^{4}}}}} + {{{{9}} {{{\phi_R}}} \cdot {{{{\phi_L}}^{2}}} {{{cos\left( {\theta_R}\right)}^{2}}}} - {{{3}} {{{\phi_R}}} \cdot {{{{\phi_L}}^{2}}} {{{cos\left( {\theta_R}\right)}^{2}}} {{{sin\left( {\theta_R}\right)}^{2}}}}} + {{{{{3}} {{{\phi_R}}} \cdot {{{{\phi_L}}^{2}}} {{{sin\left( {\theta_R}\right)}^{2}}}} - {{{6}} {{{\phi_R}}} \cdot {{{{\phi_L}}^{2}}}}} - {{{6}} {{{\phi_R}}} \cdot {{{cos\left( {\theta_R}\right)}^{2}}}}} + {{{6}} {{{\phi_R}}}} + {{{{{\phi_L}}^{3}}} {{{cos\left( {\theta_R}\right)}^{2}}} {{{sin\left( {\theta_R}\right)}^{2}}}} + {{{{{{{\phi_L}}^{3}}} {{{cos\left( {\theta_R}\right)}^{4}}}} - {{{3}} {{{{\phi_L}}^{3}}} {{{cos\left( {\theta_R}\right)}^{2}}}}} - {{{{{\phi_L}}^{3}}} {{{sin\left( {\theta_R}\right)}^{2}}}}} + {{{2}} {{{{\phi_L}}^{3}}}} + {{{{{3}} {{{{\phi_R}}^{3}}} {{{cos\left( {\theta_R}\right)}^{2}}}} - {{{{{\phi_R}}^{3}}} {{{cos\left( {\theta_R}\right)}^{4}}}}} - {{{{{\phi_R}}^{3}}} {{{sin\left( {\theta_R}\right)}^{2}}} {{{cos\left( {\theta_R}\right)}^{2}}}}} + {{{{{{\phi_R}}^{3}}} {{{sin\left( {\theta_R}\right)}^{2}}}} - {{{2}} {{{{\phi_R}}^{3}}}}}})}}}{{{6}} {{cosh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}}} \\ \frac{-{{{{({{{\phi_L}} - {{\phi_R}}})}^{2}}} {{sin\left( {\theta_R}\right)}} {{cos\left( {\theta_R}\right)}} {{cosh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}}}}{{{2}} {{w}} {{sinh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}}} & {\frac{1}{2}}{({{{{cos\left( {\theta_R}\right)}^{2}}} {{({{{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_L}}^{2}}} - {{{\phi_R}}^{2}}})}}})} & {\frac{1}{6}}{({{{sin\left( {\theta_R}\right)}} {{cos\left( {\theta_R}\right)}} {{({{{{{{3}} {{{\phi_L}}} \cdot {{{{\phi_R}}^{2}}}} - {{{6}} {{{\phi_L}}}}} - {{{3}} {{{\phi_R}}} \cdot {{{{\phi_L}}^{2}}}}} + {{{{6}} {{{\phi_R}}}} - {{{\phi_R}}^{3}}} + {{{\phi_L}}^{3}}})}}})} \\ \frac{-{{{cosh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}} {{({{{{3}} {{{\phi_L}}} \cdot {{{{\phi_R}}^{2}}}} + {{{{{\phi_L}}^{3}} - {{{6}} {{{\phi_L}}}}} - {{{3}} {{{\phi_R}}} \cdot {{{{\phi_L}}^{2}}}}} + {{{{6}} {{{\phi_R}}}} - {{{\phi_R}}^{3}}}})}}}}{{{6}} {{w}} {{sinh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}}} & \frac{-{{{cos\left( {\theta_R}\right)}} {{({{{{3}} {{{\phi_L}}} \cdot {{{{\phi_R}}^{2}}}} + {{{{{\phi_L}}^{3}} - {{{6}} {{{\phi_L}}}}} - {{{3}} {{{\phi_R}}} \cdot {{{{\phi_L}}^{2}}}}} + {{{{6}} {{{\phi_R}}}} - {{{\phi_R}}^{3}}}})}}}}{{{6}} {{sin\left( {\theta_R}\right)}}} & {\frac{1}{2}}{({-{({{{{{\phi_L}}^{2}} - {{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}}} + {{{\phi_R}}^{2}}})}})}\end{matrix}\right]} + {{\mathcal{O}(A^4)}}})}} {\left[\begin{matrix} cos\left( {{{\theta_L}} - {{\theta_R}}}\right) & \frac{-{{{w}} {{sin\left( {{{\theta_L}} - {{\theta_R}}}\right)}} {{sinh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}}}}{cosh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)} & 0 \\ \frac{{{cosh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}} {{sin\left( {{{\theta_L}} - {{\theta_R}}}\right)}}}{{{w}} {{sinh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}}} & cos\left( {{{\theta_L}} - {{\theta_R}}}\right) & 0 \\ 0 & 0 & \frac{|{sin\left( {\theta_L}\right)}|}{|{sin\left( {\theta_R}\right)}|}\end{matrix}\right]}}$ = $\left[\begin{matrix} \left[\begin{matrix} {\frac{1}{2}}{({-{{{cos\left( {{{\theta_L}} - {{\theta_R}}}\right)}} {{({{{{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}} \cdot {{{cos\left( {\theta_L}\right)}^{2}}}} - {{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}} \cdot {{{cos\left( {\theta_R}\right)}^{2}}}}} - {{{{{\phi_L}}^{2}}} {{{cos\left( {\theta_L}\right)}^{2}}}}} + {{{{{{\phi_L}}^{2}}} {{{cos\left( {\theta_R}\right)}^{2}}}} - {{{{{\phi_R}}^{2}}} {{{cos\left( {\theta_L}\right)}^{2}}}}} + {{{{{\phi_R}}^{2}}} {{{cos\left( {\theta_R}\right)}^{2}}}}})}}}})} & \frac{{{w}} {{cos\left( {{{\theta_L}} - {{\theta_R}}}\right)}} {{sinh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}} {{({{{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}} \cdot {{cos\left( {\theta_L}\right)}} {{sin\left( {\theta_L}\right)}}} - {{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}} \cdot {{cos\left( {\theta_R}\right)}} {{sin\left( {\theta_R}\right)}}}} + {{{{{{\phi_L}}^{2}}} {{cos\left( {\theta_R}\right)}} {{sin\left( {\theta_R}\right)}}} - {{{{{\phi_L}}^{2}}} {{sin\left( {\theta_L}\right)}} {{cos\left( {\theta_L}\right)}}}} + {{{{{{\phi_R}}^{2}}} {{cos\left( {\theta_R}\right)}} {{sin\left( {\theta_R}\right)}}} - {{{{{\phi_R}}^{2}}} {{sin\left( {\theta_L}\right)}} {{cos\left( {\theta_L}\right)}}}}})}}}{{{2}} {{cosh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}}} & \frac{-{{{w}} {{cos\left( {{{\theta_L}} - {{\theta_R}}}\right)}} {{sinh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}} {{({{{{{{{9}} {{{\phi_L}}} \cdot {{{{\phi_R}}^{2}}} {{{cos\left( {\theta_L}\right)}^{2}}}} - {{{3}} {{{\phi_L}}} \cdot {{{{\phi_R}}^{2}}} {{{cos\left( {\theta_L}\right)}^{4}}}}} - {{{3}} {{{\phi_L}}} \cdot {{{{\phi_R}}^{2}}} {{{cos\left( {\theta_L}\right)}^{2}}} {{{sin\left( {\theta_L}\right)}^{2}}}}} - {{{9}} {{{\phi_L}}} \cdot {{{{\phi_R}}^{2}}} {{{cos\left( {\theta_R}\right)}^{2}}}}} + {{{3}} {{{\phi_L}}} \cdot {{{{\phi_R}}^{2}}} {{{cos\left( {\theta_R}\right)}^{4}}}} + {{{3}} {{{\phi_L}}} \cdot {{{{\phi_R}}^{2}}} {{{cos\left( {\theta_R}\right)}^{2}}} {{{sin\left( {\theta_R}\right)}^{2}}}} + {{{{{3}} {{{\phi_L}}} \cdot {{{{\phi_R}}^{2}}} {{{sin\left( {\theta_L}\right)}^{2}}}} - {{{3}} {{{\phi_L}}} \cdot {{{{\phi_R}}^{2}}} {{{sin\left( {\theta_R}\right)}^{2}}}}} - {{{6}} {{{\phi_L}}} \cdot {{{cos\left( {\theta_L}\right)}^{2}}}}} + {{{{6}} {{{\phi_L}}} \cdot {{{cos\left( {\theta_R}\right)}^{2}}}} - {{{9}} {{{\phi_R}}} \cdot {{{{\phi_L}}^{2}}} {{{cos\left( {\theta_L}\right)}^{2}}}}} + {{{3}} {{{\phi_R}}} \cdot {{{{\phi_L}}^{2}}} {{{cos\left( {\theta_L}\right)}^{4}}}} + {{{{3}} {{{\phi_R}}} \cdot {{{{\phi_L}}^{2}}} {{{cos\left( {\theta_L}\right)}^{2}}} {{{sin\left( {\theta_L}\right)}^{2}}}} - {{{3}} {{{\phi_R}}} \cdot {{{{\phi_L}}^{2}}} {{{cos\left( {\theta_R}\right)}^{4}}}}} + {{{{{9}} {{{\phi_R}}} \cdot {{{{\phi_L}}^{2}}} {{{cos\left( {\theta_R}\right)}^{2}}}} - {{{3}} {{{\phi_R}}} \cdot {{{{\phi_L}}^{2}}} {{{cos\left( {\theta_R}\right)}^{2}}} {{{sin\left( {\theta_R}\right)}^{2}}}}} - {{{3}} {{{\phi_R}}} \cdot {{{{\phi_L}}^{2}}} {{{sin\left( {\theta_L}\right)}^{2}}}}} + {{{3}} {{{\phi_R}}} \cdot {{{{\phi_L}}^{2}}} {{{sin\left( {\theta_R}\right)}^{2}}}} + {{{{6}} {{{\phi_R}}} \cdot {{{cos\left( {\theta_L}\right)}^{2}}}} - {{{6}} {{{\phi_R}}} \cdot {{{cos\left( {\theta_R}\right)}^{2}}}}} + {{{{{3}} {{{{\phi_L}}^{3}}} {{{cos\left( {\theta_L}\right)}^{2}}}} - {{{{{\phi_L}}^{3}}} {{{cos\left( {\theta_L}\right)}^{4}}}}} - {{{{{\phi_L}}^{3}}} {{{sin\left( {\theta_L}\right)}^{2}}} {{{cos\left( {\theta_L}\right)}^{2}}}}} + {{{{{{\phi_L}}^{3}}} {{{cos\left( {\theta_R}\right)}^{4}}}} - {{{3}} {{{{\phi_L}}^{3}}} {{{cos\left( {\theta_R}\right)}^{2}}}}} + {{{{{{\phi_L}}^{3}}} {{{sin\left( {\theta_L}\right)}^{2}}}} - {{{{{\phi_L}}^{3}}} {{{sin\left( {\theta_R}\right)}^{2}}}}} + {{{{{{\phi_L}}^{3}}} {{{cos\left( {\theta_R}\right)}^{2}}} {{{sin\left( {\theta_R}\right)}^{2}}}} - {{{3}} {{{{\phi_R}}^{3}}} {{{cos\left( {\theta_L}\right)}^{2}}}}} + {{{{{{{\phi_R}}^{3}}} {{{cos\left( {\theta_L}\right)}^{4}}}} - {{{{{\phi_R}}^{3}}} {{{cos\left( {\theta_R}\right)}^{4}}}}} - {{{{{\phi_R}}^{3}}} {{{sin\left( {\theta_R}\right)}^{2}}} {{{cos\left( {\theta_R}\right)}^{2}}}}} + {{{{3}} {{{{\phi_R}}^{3}}} {{{cos\left( {\theta_R}\right)}^{2}}}} - {{{{{\phi_R}}^{3}}} {{{sin\left( {\theta_L}\right)}^{2}}}}} + {{{{{\phi_R}}^{3}}} {{{cos\left( {\theta_L}\right)}^{2}}} {{{sin\left( {\theta_L}\right)}^{2}}}} + {{{{{\phi_R}}^{3}}} {{{sin\left( {\theta_R}\right)}^{2}}}}})}}}}{{{6}} {{cosh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}}} \\ \frac{{{cos\left( {{{\theta_L}} - {{\theta_R}}}\right)}} {{cosh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}} {{({{{{{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}} \cdot {{cos\left( {\theta_L}\right)}} {{sin\left( {\theta_L}\right)}}} - {{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}} \cdot {{cos\left( {\theta_R}\right)}} {{sin\left( {\theta_R}\right)}}}} - {{{{{\phi_L}}^{2}}} {{sin\left( {\theta_L}\right)}} {{cos\left( {\theta_L}\right)}}}} - {{{{{\phi_R}}^{2}}} {{sin\left( {\theta_L}\right)}} {{cos\left( {\theta_L}\right)}}}} + {{{{{\phi_L}}^{2}}} {{cos\left( {\theta_R}\right)}} {{sin\left( {\theta_R}\right)}}} + {{{{{\phi_R}}^{2}}} {{cos\left( {\theta_R}\right)}} {{sin\left( {\theta_R}\right)}}}})}}}{{{2}} {{w}} {{sinh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}}} & {\frac{1}{2}}{({{{cos\left( {{{\theta_L}} - {{\theta_R}}}\right)}} {{({{{{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}} \cdot {{{cos\left( {\theta_L}\right)}^{2}}}} - {{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}} \cdot {{{cos\left( {\theta_R}\right)}^{2}}}}} - {{{{{\phi_L}}^{2}}} {{{cos\left( {\theta_L}\right)}^{2}}}}} + {{{{{{\phi_L}}^{2}}} {{{cos\left( {\theta_R}\right)}^{2}}}} - {{{{{\phi_R}}^{2}}} {{{cos\left( {\theta_L}\right)}^{2}}}}} + {{{{{\phi_R}}^{2}}} {{{cos\left( {\theta_R}\right)}^{2}}}}})}}})} & {\frac{1}{6}}{({{{cos\left( {{{\theta_L}} - {{\theta_R}}}\right)}} {{({{{{{{{3}} {{{\phi_L}}} \cdot {{{{\phi_R}}^{2}}} {{cos\left( {\theta_L}\right)}} {{sin\left( {\theta_L}\right)}}} - {{{3}} {{{\phi_L}}} \cdot {{{{\phi_R}}^{2}}} {{cos\left( {\theta_R}\right)}} {{sin\left( {\theta_R}\right)}}}} - {{{6}} {{{\phi_L}}} \cdot {{sin\left( {\theta_L}\right)}} {{cos\left( {\theta_L}\right)}}}} - {{{{{\phi_L}}^{3}}} {{sin\left( {\theta_R}\right)}} {{cos\left( {\theta_R}\right)}}}} + {{{6}} {{{\phi_L}}} \cdot {{sin\left( {\theta_R}\right)}} {{cos\left( {\theta_R}\right)}}} + {{{{{{\phi_L}}^{3}}} {{cos\left( {\theta_L}\right)}} {{sin\left( {\theta_L}\right)}}} - {{{3}} {{{\phi_R}}} \cdot {{{{\phi_L}}^{2}}} {{cos\left( {\theta_L}\right)}} {{sin\left( {\theta_L}\right)}}}} + {{{3}} {{{\phi_R}}} \cdot {{{{\phi_L}}^{2}}} {{cos\left( {\theta_R}\right)}} {{sin\left( {\theta_R}\right)}}} + {{{{{6}} {{{\phi_R}}} \cdot {{sin\left( {\theta_L}\right)}} {{cos\left( {\theta_L}\right)}}} - {{{{{\phi_R}}^{3}}} {{sin\left( {\theta_L}\right)}} {{cos\left( {\theta_L}\right)}}}} - {{{6}} {{{\phi_R}}} \cdot {{sin\left( {\theta_R}\right)}} {{cos\left( {\theta_R}\right)}}}} + {{{{{\phi_R}}^{3}}} {{cos\left( {\theta_R}\right)}} {{sin\left( {\theta_R}\right)}}}})}}})} \\ 0 & \frac{-{{{cos\left( {{{\theta_L}} - {{\theta_R}}}\right)}} {{({{{{{3}} {{{\phi_L}}} \cdot {{{{\phi_R}}^{2}}} {{cos\left( {\theta_L}\right)}} {{sin\left( {\theta_R}\right)}}} - {{{3}} {{{\phi_L}}} \cdot {{{{\phi_R}}^{2}}} {{cos\left( {\theta_R}\right)}} {{sin\left( {\theta_L}\right)}}}} + {{{{6}} {{{\phi_L}}} \cdot {{sin\left( {\theta_L}\right)}} {{cos\left( {\theta_R}\right)}}} - {{{6}} {{{\phi_L}}} \cdot {{sin\left( {\theta_R}\right)}} {{cos\left( {\theta_L}\right)}}}} + {{{{{{{\phi_L}}^{3}}} {{cos\left( {\theta_L}\right)}} {{sin\left( {\theta_R}\right)}}} - {{{{{\phi_L}}^{3}}} {{sin\left( {\theta_L}\right)}} {{cos\left( {\theta_R}\right)}}}} - {{{3}} {{{\phi_R}}} \cdot {{{{\phi_L}}^{2}}} {{cos\left( {\theta_L}\right)}} {{sin\left( {\theta_R}\right)}}}} + {{{3}} {{{\phi_R}}} \cdot {{{{\phi_L}}^{2}}} {{cos\left( {\theta_R}\right)}} {{sin\left( {\theta_L}\right)}}} + {{{{{{\phi_R}}^{3}}} {{cos\left( {\theta_R}\right)}} {{sin\left( {\theta_L}\right)}}} - {{{6}} {{{\phi_R}}} \cdot {{sin\left( {\theta_L}\right)}} {{cos\left( {\theta_R}\right)}}}} + {{{{6}} {{{\phi_R}}} \cdot {{sin\left( {\theta_R}\right)}} {{cos\left( {\theta_L}\right)}}} - {{{{{\phi_R}}^{3}}} {{sin\left( {\theta_R}\right)}} {{cos\left( {\theta_L}\right)}}}}})}}}}{{{6}} {{sin\left( {\theta_R}\right)}} {{sin\left( {\theta_L}\right)}}} & 0\end{matrix}\right] & \left[\begin{matrix} \frac{{{w}} {{sin\left( {{{\theta_L}} - {{\theta_R}}}\right)}} {{sinh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}} {{({{{{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}} \cdot {{{cos\left( {\theta_L}\right)}^{2}}}} - {{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}} \cdot {{{cos\left( {\theta_R}\right)}^{2}}}}} - {{{{{\phi_L}}^{2}}} {{{cos\left( {\theta_L}\right)}^{2}}}}} + {{{{{{\phi_L}}^{2}}} {{{cos\left( {\theta_R}\right)}^{2}}}} - {{{{{\phi_R}}^{2}}} {{{cos\left( {\theta_L}\right)}^{2}}}}} + {{{{{\phi_R}}^{2}}} {{{cos\left( {\theta_R}\right)}^{2}}}}})}}}{{{2}} {{cosh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}}} & \frac{-{{{{w}^{2}}} {{{sinh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}^{2}}} {{sin\left( {{{\theta_L}} - {{\theta_R}}}\right)}} {{({{{{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}} \cdot {{cos\left( {\theta_L}\right)}} {{sin\left( {\theta_L}\right)}}} - {{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}} \cdot {{cos\left( {\theta_R}\right)}} {{sin\left( {\theta_R}\right)}}}} - {{{{{\phi_L}}^{2}}} {{sin\left( {\theta_L}\right)}} {{cos\left( {\theta_L}\right)}}}} + {{{{{{\phi_L}}^{2}}} {{cos\left( {\theta_R}\right)}} {{sin\left( {\theta_R}\right)}}} - {{{{{\phi_R}}^{2}}} {{sin\left( {\theta_L}\right)}} {{cos\left( {\theta_L}\right)}}}} + {{{{{\phi_R}}^{2}}} {{cos\left( {\theta_R}\right)}} {{sin\left( {\theta_R}\right)}}}})}}}}{{{2}} {{{cosh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}^{2}}}} & \frac{{{{w}^{2}}} {{{sinh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}^{2}}} {{sin\left( {{{\theta_L}} - {{\theta_R}}}\right)}} {{({{{{{{9}} {{{\phi_L}}} \cdot {{{{\phi_R}}^{2}}} {{{cos\left( {\theta_L}\right)}^{2}}}} - {{{9}} {{{\phi_L}}} \cdot {{{{\phi_R}}^{2}}} {{{cos\left( {\theta_R}\right)}^{2}}}}} - {{{3}} {{{\phi_L}}} \cdot {{{{\phi_R}}^{2}}} {{{cos\left( {\theta_L}\right)}^{2}}} {{{sin\left( {\theta_L}\right)}^{2}}}}} + {{{3}} {{{\phi_L}}} \cdot {{{{\phi_R}}^{2}}} {{{sin\left( {\theta_L}\right)}^{2}}}} + {{{{{3}} {{{\phi_L}}} \cdot {{{{\phi_R}}^{2}}} {{{cos\left( {\theta_R}\right)}^{2}}} {{{sin\left( {\theta_R}\right)}^{2}}}} - {{{3}} {{{\phi_L}}} \cdot {{{{\phi_R}}^{2}}} {{{sin\left( {\theta_R}\right)}^{2}}}}} - {{{3}} {{{\phi_L}}} \cdot {{{{\phi_R}}^{2}}} {{{cos\left( {\theta_L}\right)}^{4}}}}} + {{{3}} {{{\phi_L}}} \cdot {{{{\phi_R}}^{2}}} {{{cos\left( {\theta_R}\right)}^{4}}}} + {{{{{3}} {{{{\phi_L}}^{3}}} {{{cos\left( {\theta_L}\right)}^{2}}}} - {{{6}} {{{\phi_L}}} \cdot {{{cos\left( {\theta_L}\right)}^{2}}}}} - {{{3}} {{{{\phi_L}}^{3}}} {{{cos\left( {\theta_R}\right)}^{2}}}}} + {{{6}} {{{\phi_L}}} \cdot {{{cos\left( {\theta_R}\right)}^{2}}}} + {{{{{{\phi_L}}^{3}}} {{{cos\left( {\theta_R}\right)}^{2}}} {{{sin\left( {\theta_R}\right)}^{2}}}} - {{{{{\phi_L}}^{3}}} {{{sin\left( {\theta_L}\right)}^{2}}} {{{cos\left( {\theta_L}\right)}^{2}}}}} + {{{{{{{\phi_L}}^{3}}} {{{sin\left( {\theta_L}\right)}^{2}}}} - {{{{{\phi_L}}^{3}}} {{{sin\left( {\theta_R}\right)}^{2}}}}} - {{{{{\phi_L}}^{3}}} {{{cos\left( {\theta_L}\right)}^{4}}}}} + {{{{{{\phi_L}}^{3}}} {{{cos\left( {\theta_R}\right)}^{4}}}} - {{{9}} {{{\phi_R}}} \cdot {{{{\phi_L}}^{2}}} {{{cos\left( {\theta_L}\right)}^{2}}}}} + {{{9}} {{{\phi_R}}} \cdot {{{{\phi_L}}^{2}}} {{{cos\left( {\theta_R}\right)}^{2}}}} + {{{{{3}} {{{\phi_R}}} \cdot {{{{\phi_L}}^{2}}} {{{cos\left( {\theta_L}\right)}^{2}}} {{{sin\left( {\theta_L}\right)}^{2}}}} - {{{3}} {{{\phi_R}}} \cdot {{{{\phi_L}}^{2}}} {{{sin\left( {\theta_L}\right)}^{2}}}}} - {{{3}} {{{\phi_R}}} \cdot {{{{\phi_L}}^{2}}} {{{cos\left( {\theta_R}\right)}^{2}}} {{{sin\left( {\theta_R}\right)}^{2}}}}} + {{{3}} {{{\phi_R}}} \cdot {{{{\phi_L}}^{2}}} {{{sin\left( {\theta_R}\right)}^{2}}}} + {{{{{3}} {{{\phi_R}}} \cdot {{{{\phi_L}}^{2}}} {{{cos\left( {\theta_L}\right)}^{4}}}} - {{{3}} {{{\phi_R}}} \cdot {{{{\phi_L}}^{2}}} {{{cos\left( {\theta_R}\right)}^{4}}}}} - {{{3}} {{{{\phi_R}}^{3}}} {{{cos\left( {\theta_L}\right)}^{2}}}}} + {{{6}} {{{\phi_R}}} \cdot {{{cos\left( {\theta_L}\right)}^{2}}}} + {{{{{\phi_R}}^{3}}} {{{cos\left( {\theta_L}\right)}^{2}}} {{{sin\left( {\theta_L}\right)}^{2}}}} + {{{{{{3}} {{{{\phi_R}}^{3}}} {{{cos\left( {\theta_R}\right)}^{2}}}} - {{{6}} {{{\phi_R}}} \cdot {{{cos\left( {\theta_R}\right)}^{2}}}}} - {{{{{\phi_R}}^{3}}} {{{sin\left( {\theta_L}\right)}^{2}}}}} - {{{{{\phi_R}}^{3}}} {{{sin\left( {\theta_R}\right)}^{2}}} {{{cos\left( {\theta_R}\right)}^{2}}}}} + {{{{{\phi_R}}^{3}}} {{{sin\left( {\theta_R}\right)}^{2}}}} + {{{{{{\phi_R}}^{3}}} {{{cos\left( {\theta_L}\right)}^{4}}}} - {{{{{\phi_R}}^{3}}} {{{cos\left( {\theta_R}\right)}^{4}}}}}})}}}{{{6}} {{{cosh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}^{2}}}} \\ {\frac{1}{2}}{({-{{{sin\left( {{{\theta_L}} - {{\theta_R}}}\right)}} {{({{{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}} \cdot {{cos\left( {\theta_L}\right)}} {{sin\left( {\theta_L}\right)}}} - {{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}} \cdot {{cos\left( {\theta_R}\right)}} {{sin\left( {\theta_R}\right)}}}} + {{{{{{\phi_L}}^{2}}} {{cos\left( {\theta_R}\right)}} {{sin\left( {\theta_R}\right)}}} - {{{{{\phi_L}}^{2}}} {{sin\left( {\theta_L}\right)}} {{cos\left( {\theta_L}\right)}}}} + {{{{{{\phi_R}}^{2}}} {{cos\left( {\theta_R}\right)}} {{sin\left( {\theta_R}\right)}}} - {{{{{\phi_R}}^{2}}} {{sin\left( {\theta_L}\right)}} {{cos\left( {\theta_L}\right)}}}}})}}}})} & \frac{-{{{w}} {{sin\left( {{{\theta_L}} - {{\theta_R}}}\right)}} {{sinh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}} {{({{{{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}} \cdot {{{cos\left( {\theta_L}\right)}^{2}}}} - {{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}} \cdot {{{cos\left( {\theta_R}\right)}^{2}}}}} - {{{{{\phi_L}}^{2}}} {{{cos\left( {\theta_L}\right)}^{2}}}}} + {{{{{{\phi_L}}^{2}}} {{{cos\left( {\theta_R}\right)}^{2}}}} - {{{{{\phi_R}}^{2}}} {{{cos\left( {\theta_L}\right)}^{2}}}}} + {{{{{\phi_R}}^{2}}} {{{cos\left( {\theta_R}\right)}^{2}}}}})}}}}{{{2}} {{cosh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}}} & \frac{-{{{w}} {{sin\left( {{{\theta_L}} - {{\theta_R}}}\right)}} {{sinh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}} {{({{{{{{3}} {{{\phi_L}}} \cdot {{{{\phi_R}}^{2}}} {{cos\left( {\theta_L}\right)}} {{sin\left( {\theta_L}\right)}}} - {{{3}} {{{\phi_L}}} \cdot {{{{\phi_R}}^{2}}} {{cos\left( {\theta_R}\right)}} {{sin\left( {\theta_R}\right)}}}} - {{{{{\phi_L}}^{3}}} {{sin\left( {\theta_R}\right)}} {{cos\left( {\theta_R}\right)}}}} + {{{{{{\phi_L}}^{3}}} {{cos\left( {\theta_L}\right)}} {{sin\left( {\theta_L}\right)}}} - {{{6}} {{{\phi_L}}} \cdot {{sin\left( {\theta_L}\right)}} {{cos\left( {\theta_L}\right)}}}} + {{{{6}} {{{\phi_L}}} \cdot {{sin\left( {\theta_R}\right)}} {{cos\left( {\theta_R}\right)}}} - {{{3}} {{{\phi_R}}} \cdot {{{{\phi_L}}^{2}}} {{cos\left( {\theta_L}\right)}} {{sin\left( {\theta_L}\right)}}}} + {{{{3}} {{{\phi_R}}} \cdot {{{{\phi_L}}^{2}}} {{cos\left( {\theta_R}\right)}} {{sin\left( {\theta_R}\right)}}} - {{{{{\phi_R}}^{3}}} {{sin\left( {\theta_L}\right)}} {{cos\left( {\theta_L}\right)}}}} + {{{{6}} {{{\phi_R}}} \cdot {{sin\left( {\theta_L}\right)}} {{cos\left( {\theta_L}\right)}}} - {{{6}} {{{\phi_R}}} \cdot {{sin\left( {\theta_R}\right)}} {{cos\left( {\theta_R}\right)}}}} + {{{{{\phi_R}}^{3}}} {{cos\left( {\theta_R}\right)}} {{sin\left( {\theta_R}\right)}}}})}}}}{{{6}} {{cosh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}}} \\ 0 & \frac{-{{{w}} {{sin\left( {{{\theta_L}} - {{\theta_R}}}\right)}} {{sinh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}} {{({{{{{{3}} {{{\phi_L}}} \cdot {{{{\phi_R}}^{2}}} {{cos\left( {\theta_R}\right)}} {{sin\left( {\theta_L}\right)}}} - {{{3}} {{{\phi_L}}} \cdot {{{{\phi_R}}^{2}}} {{cos\left( {\theta_L}\right)}} {{sin\left( {\theta_R}\right)}}}} - {{{{{\phi_L}}^{3}}} {{sin\left( {\theta_R}\right)}} {{cos\left( {\theta_L}\right)}}}} + {{{6}} {{{\phi_L}}} \cdot {{sin\left( {\theta_R}\right)}} {{cos\left( {\theta_L}\right)}}} + {{{{{{{\phi_L}}^{3}}} {{cos\left( {\theta_R}\right)}} {{sin\left( {\theta_L}\right)}}} - {{{6}} {{{\phi_L}}} \cdot {{sin\left( {\theta_L}\right)}} {{cos\left( {\theta_R}\right)}}}} - {{{3}} {{{\phi_R}}} \cdot {{{{\phi_L}}^{2}}} {{cos\left( {\theta_R}\right)}} {{sin\left( {\theta_L}\right)}}}} + {{{{{3}} {{{\phi_R}}} \cdot {{{{\phi_L}}^{2}}} {{cos\left( {\theta_L}\right)}} {{sin\left( {\theta_R}\right)}}} - {{{{{\phi_R}}^{3}}} {{sin\left( {\theta_L}\right)}} {{cos\left( {\theta_R}\right)}}}} - {{{6}} {{{\phi_R}}} \cdot {{sin\left( {\theta_R}\right)}} {{cos\left( {\theta_L}\right)}}}} + {{{{{\phi_R}}^{3}}} {{cos\left( {\theta_L}\right)}} {{sin\left( {\theta_R}\right)}}} + {{{6}} {{{\phi_R}}} \cdot {{sin\left( {\theta_L}\right)}} {{cos\left( {\theta_R}\right)}}}})}}}}{{{6}} {{sin\left( {\theta_L}\right)}} {{sin\left( {\theta_R}\right)}} {{cosh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}}} & 0\end{matrix}\right] & 0 \\ \left[\begin{matrix} \frac{-{{{sin\left( {{{\theta_L}} - {{\theta_R}}}\right)}} {{cosh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}} {{({{{{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}} \cdot {{{cos\left( {\theta_L}\right)}^{2}}}} - {{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}} \cdot {{{cos\left( {\theta_R}\right)}^{2}}}}} - {{{{{\phi_L}}^{2}}} {{{cos\left( {\theta_L}\right)}^{2}}}}} + {{{{{{\phi_L}}^{2}}} {{{cos\left( {\theta_R}\right)}^{2}}}} - {{{{{\phi_R}}^{2}}} {{{cos\left( {\theta_L}\right)}^{2}}}}} + {{{{{\phi_R}}^{2}}} {{{cos\left( {\theta_R}\right)}^{2}}}}})}}}}{{{2}} {{w}} {{sinh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}}} & {\frac{1}{2}}{({{{sin\left( {{{\theta_L}} - {{\theta_R}}}\right)}} {{({{{{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}} \cdot {{cos\left( {\theta_L}\right)}} {{sin\left( {\theta_L}\right)}}} - {{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}} \cdot {{cos\left( {\theta_R}\right)}} {{sin\left( {\theta_R}\right)}}}} - {{{{{\phi_L}}^{2}}} {{sin\left( {\theta_L}\right)}} {{cos\left( {\theta_L}\right)}}}} + {{{{{{\phi_L}}^{2}}} {{cos\left( {\theta_R}\right)}} {{sin\left( {\theta_R}\right)}}} - {{{{{\phi_R}}^{2}}} {{sin\left( {\theta_L}\right)}} {{cos\left( {\theta_L}\right)}}}} + {{{{{\phi_R}}^{2}}} {{cos\left( {\theta_R}\right)}} {{sin\left( {\theta_R}\right)}}}})}}})} & {\frac{1}{6}}{({{{sin\left( {{{\theta_L}} - {{\theta_R}}}\right)}} {{({{{{{3}} {{{\phi_L}}} \cdot {{{{\phi_R}}^{2}}} {{{cos\left( {\theta_L}\right)}^{4}}}} - {{{9}} {{{\phi_L}}} \cdot {{{{\phi_R}}^{2}}} {{{cos\left( {\theta_L}\right)}^{2}}}}} + {{{{9}} {{{\phi_L}}} \cdot {{{{\phi_R}}^{2}}} {{{cos\left( {\theta_R}\right)}^{2}}}} - {{{3}} {{{\phi_L}}} \cdot {{{{\phi_R}}^{2}}} {{{cos\left( {\theta_R}\right)}^{4}}}}} + {{{{{3}} {{{\phi_L}}} \cdot {{{{\phi_R}}^{2}}} {{{cos\left( {\theta_L}\right)}^{2}}} {{{sin\left( {\theta_L}\right)}^{2}}}} - {{{3}} {{{\phi_L}}} \cdot {{{{\phi_R}}^{2}}} {{{sin\left( {\theta_L}\right)}^{2}}}}} - {{{3}} {{{\phi_L}}} \cdot {{{{\phi_R}}^{2}}} {{{cos\left( {\theta_R}\right)}^{2}}} {{{sin\left( {\theta_R}\right)}^{2}}}}} + {{{{3}} {{{\phi_L}}} \cdot {{{{\phi_R}}^{2}}} {{{sin\left( {\theta_R}\right)}^{2}}}} - {{{3}} {{{{\phi_L}}^{3}}} {{{cos\left( {\theta_L}\right)}^{2}}}}} + {{{{{\phi_L}}^{3}}} {{{cos\left( {\theta_L}\right)}^{4}}}} + {{{6}} {{{\phi_L}}} \cdot {{{cos\left( {\theta_L}\right)}^{2}}}} + {{{{{{3}} {{{{\phi_L}}^{3}}} {{{cos\left( {\theta_R}\right)}^{2}}}} - {{{6}} {{{\phi_L}}} \cdot {{{cos\left( {\theta_R}\right)}^{2}}}}} - {{{{{\phi_L}}^{3}}} {{{cos\left( {\theta_R}\right)}^{4}}}}} - {{{{{\phi_L}}^{3}}} {{{sin\left( {\theta_R}\right)}^{2}}} {{{cos\left( {\theta_R}\right)}^{2}}}}} + {{{{{{\phi_L}}^{3}}} {{{cos\left( {\theta_L}\right)}^{2}}} {{{sin\left( {\theta_L}\right)}^{2}}}} - {{{{{\phi_L}}^{3}}} {{{sin\left( {\theta_L}\right)}^{2}}}}} + {{{{{\phi_L}}^{3}}} {{{sin\left( {\theta_R}\right)}^{2}}}} + {{{{{9}} {{{\phi_R}}} \cdot {{{{\phi_L}}^{2}}} {{{cos\left( {\theta_L}\right)}^{2}}}} - {{{3}} {{{\phi_R}}} \cdot {{{{\phi_L}}^{2}}} {{{cos\left( {\theta_L}\right)}^{4}}}}} - {{{9}} {{{\phi_R}}} \cdot {{{{\phi_L}}^{2}}} {{{cos\left( {\theta_R}\right)}^{2}}}}} + {{{{3}} {{{\phi_R}}} \cdot {{{{\phi_L}}^{2}}} {{{cos\left( {\theta_R}\right)}^{4}}}} - {{{3}} {{{\phi_R}}} \cdot {{{{\phi_L}}^{2}}} {{{cos\left( {\theta_L}\right)}^{2}}} {{{sin\left( {\theta_L}\right)}^{2}}}}} + {{{3}} {{{\phi_R}}} \cdot {{{{\phi_L}}^{2}}} {{{sin\left( {\theta_L}\right)}^{2}}}} + {{{{3}} {{{\phi_R}}} \cdot {{{{\phi_L}}^{2}}} {{{cos\left( {\theta_R}\right)}^{2}}} {{{sin\left( {\theta_R}\right)}^{2}}}} - {{{3}} {{{\phi_R}}} \cdot {{{{\phi_L}}^{2}}} {{{sin\left( {\theta_R}\right)}^{2}}}}} + {{{{{{3}} {{{{\phi_R}}^{3}}} {{{cos\left( {\theta_L}\right)}^{2}}}} - {{{6}} {{{\phi_R}}} \cdot {{{cos\left( {\theta_L}\right)}^{2}}}}} - {{{{{\phi_R}}^{3}}} {{{cos\left( {\theta_L}\right)}^{4}}}}} - {{{{{\phi_R}}^{3}}} {{{sin\left( {\theta_L}\right)}^{2}}} {{{cos\left( {\theta_L}\right)}^{2}}}}} + {{{{6}} {{{\phi_R}}} \cdot {{{cos\left( {\theta_R}\right)}^{2}}}} - {{{3}} {{{{\phi_R}}^{3}}} {{{cos\left( {\theta_R}\right)}^{2}}}}} + {{{{{\phi_R}}^{3}}} {{{cos\left( {\theta_R}\right)}^{4}}}} + {{{{{\phi_R}}^{3}}} {{{sin\left( {\theta_L}\right)}^{2}}}} + {{{{{{\phi_R}}^{3}}} {{{cos\left( {\theta_R}\right)}^{2}}} {{{sin\left( {\theta_R}\right)}^{2}}}} - {{{{{\phi_R}}^{3}}} {{{sin\left( {\theta_R}\right)}^{2}}}}}})}}})} \\ \frac{{{{cosh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}^{2}}} {{sin\left( {{{\theta_L}} - {{\theta_R}}}\right)}} {{({{{{{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}} \cdot {{cos\left( {\theta_L}\right)}} {{sin\left( {\theta_L}\right)}}} - {{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}} \cdot {{cos\left( {\theta_R}\right)}} {{sin\left( {\theta_R}\right)}}}} - {{{{{\phi_L}}^{2}}} {{sin\left( {\theta_L}\right)}} {{cos\left( {\theta_L}\right)}}}} - {{{{{\phi_R}}^{2}}} {{sin\left( {\theta_L}\right)}} {{cos\left( {\theta_L}\right)}}}} + {{{{{\phi_L}}^{2}}} {{cos\left( {\theta_R}\right)}} {{sin\left( {\theta_R}\right)}}} + {{{{{\phi_R}}^{2}}} {{cos\left( {\theta_R}\right)}} {{sin\left( {\theta_R}\right)}}}})}}}{{{2}} {{{w}^{2}}} {{{sinh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}^{2}}}} & \frac{{{cosh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}} {{sin\left( {{{\theta_L}} - {{\theta_R}}}\right)}} {{({{{{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}} \cdot {{{cos\left( {\theta_L}\right)}^{2}}}} - {{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}} \cdot {{{cos\left( {\theta_R}\right)}^{2}}}}} - {{{{{\phi_L}}^{2}}} {{{cos\left( {\theta_L}\right)}^{2}}}}} + {{{{{{\phi_L}}^{2}}} {{{cos\left( {\theta_R}\right)}^{2}}}} - {{{{{\phi_R}}^{2}}} {{{cos\left( {\theta_L}\right)}^{2}}}}} + {{{{{\phi_R}}^{2}}} {{{cos\left( {\theta_R}\right)}^{2}}}}})}}}{{{2}} {{w}} {{sinh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}}} & \frac{{{cosh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}} {{sin\left( {{{\theta_L}} - {{\theta_R}}}\right)}} {{({{{{{{{3}} {{{\phi_L}}} \cdot {{{{\phi_R}}^{2}}} {{cos\left( {\theta_L}\right)}} {{sin\left( {\theta_L}\right)}}} - {{{3}} {{{\phi_L}}} \cdot {{{{\phi_R}}^{2}}} {{cos\left( {\theta_R}\right)}} {{sin\left( {\theta_R}\right)}}}} - {{{6}} {{{\phi_L}}} \cdot {{sin\left( {\theta_L}\right)}} {{cos\left( {\theta_L}\right)}}}} - {{{{{\phi_L}}^{3}}} {{sin\left( {\theta_R}\right)}} {{cos\left( {\theta_R}\right)}}}} + {{{{6}} {{{\phi_L}}} \cdot {{sin\left( {\theta_R}\right)}} {{cos\left( {\theta_R}\right)}}} - {{{3}} {{{\phi_R}}} \cdot {{{{\phi_L}}^{2}}} {{cos\left( {\theta_L}\right)}} {{sin\left( {\theta_L}\right)}}}} + {{{{3}} {{{\phi_R}}} \cdot {{{{\phi_L}}^{2}}} {{cos\left( {\theta_R}\right)}} {{sin\left( {\theta_R}\right)}}} - {{{{{\phi_R}}^{3}}} {{sin\left( {\theta_L}\right)}} {{cos\left( {\theta_L}\right)}}}} + {{{{6}} {{{\phi_R}}} \cdot {{sin\left( {\theta_L}\right)}} {{cos\left( {\theta_L}\right)}}} - {{{6}} {{{\phi_R}}} \cdot {{sin\left( {\theta_R}\right)}} {{cos\left( {\theta_R}\right)}}}} + {{{{{\phi_L}}^{3}}} {{cos\left( {\theta_L}\right)}} {{sin\left( {\theta_L}\right)}}} + {{{{{\phi_R}}^{3}}} {{cos\left( {\theta_R}\right)}} {{sin\left( {\theta_R}\right)}}}})}}}{{{6}} {{w}} {{sinh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}}} \\ 0 & \frac{-{{{sin\left( {{{\theta_L}} - {{\theta_R}}}\right)}} {{cosh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}} {{({{{{{3}} {{{\phi_L}}} \cdot {{{{\phi_R}}^{2}}} {{cos\left( {\theta_L}\right)}} {{sin\left( {\theta_R}\right)}}} - {{{3}} {{{\phi_L}}} \cdot {{{{\phi_R}}^{2}}} {{cos\left( {\theta_R}\right)}} {{sin\left( {\theta_L}\right)}}}} + {{{{6}} {{{\phi_L}}} \cdot {{sin\left( {\theta_L}\right)}} {{cos\left( {\theta_R}\right)}}} - {{{6}} {{{\phi_L}}} \cdot {{sin\left( {\theta_R}\right)}} {{cos\left( {\theta_L}\right)}}}} + {{{{{{\phi_L}}^{3}}} {{cos\left( {\theta_L}\right)}} {{sin\left( {\theta_R}\right)}}} - {{{3}} {{{\phi_R}}} \cdot {{{{\phi_L}}^{2}}} {{cos\left( {\theta_L}\right)}} {{sin\left( {\theta_R}\right)}}}} + {{{3}} {{{\phi_R}}} \cdot {{{{\phi_L}}^{2}}} {{cos\left( {\theta_R}\right)}} {{sin\left( {\theta_L}\right)}}} + {{{{{{\phi_R}}^{3}}} {{cos\left( {\theta_R}\right)}} {{sin\left( {\theta_L}\right)}}} - {{{6}} {{{\phi_R}}} \cdot {{sin\left( {\theta_L}\right)}} {{cos\left( {\theta_R}\right)}}}} + {{{{{6}} {{{\phi_R}}} \cdot {{sin\left( {\theta_R}\right)}} {{cos\left( {\theta_L}\right)}}} - {{{{{\phi_L}}^{3}}} {{sin\left( {\theta_L}\right)}} {{cos\left( {\theta_R}\right)}}}} - {{{{{\phi_R}}^{3}}} {{sin\left( {\theta_R}\right)}} {{cos\left( {\theta_L}\right)}}}}})}}}}{{{6}} {{w}} {{sin\left( {\theta_L}\right)}} {{sin\left( {\theta_R}\right)}} {{sinh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}}} & 0\end{matrix}\right] & \left[\begin{matrix} {\frac{1}{2}}{({-{{{cos\left( {{{\theta_L}} - {{\theta_R}}}\right)}} {{({{{{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}} \cdot {{{cos\left( {\theta_L}\right)}^{2}}}} - {{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}} \cdot {{{cos\left( {\theta_R}\right)}^{2}}}}} - {{{{{\phi_L}}^{2}}} {{{cos\left( {\theta_L}\right)}^{2}}}}} + {{{{{{\phi_L}}^{2}}} {{{cos\left( {\theta_R}\right)}^{2}}}} - {{{{{\phi_R}}^{2}}} {{{cos\left( {\theta_L}\right)}^{2}}}}} + {{{{{\phi_R}}^{2}}} {{{cos\left( {\theta_R}\right)}^{2}}}}})}}}})} & \frac{{{w}} {{cos\left( {{{\theta_L}} - {{\theta_R}}}\right)}} {{sinh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}} {{({{{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}} \cdot {{cos\left( {\theta_L}\right)}} {{sin\left( {\theta_L}\right)}}} - {{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}} \cdot {{cos\left( {\theta_R}\right)}} {{sin\left( {\theta_R}\right)}}}} + {{{{{{\phi_L}}^{2}}} {{cos\left( {\theta_R}\right)}} {{sin\left( {\theta_R}\right)}}} - {{{{{\phi_L}}^{2}}} {{sin\left( {\theta_L}\right)}} {{cos\left( {\theta_L}\right)}}}} + {{{{{{\phi_R}}^{2}}} {{cos\left( {\theta_R}\right)}} {{sin\left( {\theta_R}\right)}}} - {{{{{\phi_R}}^{2}}} {{sin\left( {\theta_L}\right)}} {{cos\left( {\theta_L}\right)}}}}})}}}{{{2}} {{cosh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}}} & \frac{-{{{w}} {{cos\left( {{{\theta_L}} - {{\theta_R}}}\right)}} {{sinh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}} {{({{{{{{{9}} {{{\phi_L}}} \cdot {{{{\phi_R}}^{2}}} {{{cos\left( {\theta_L}\right)}^{2}}}} - {{{3}} {{{\phi_L}}} \cdot {{{{\phi_R}}^{2}}} {{{cos\left( {\theta_L}\right)}^{4}}}}} - {{{3}} {{{\phi_L}}} \cdot {{{{\phi_R}}^{2}}} {{{cos\left( {\theta_L}\right)}^{2}}} {{{sin\left( {\theta_L}\right)}^{2}}}}} - {{{9}} {{{\phi_L}}} \cdot {{{{\phi_R}}^{2}}} {{{cos\left( {\theta_R}\right)}^{2}}}}} + {{{3}} {{{\phi_L}}} \cdot {{{{\phi_R}}^{2}}} {{{cos\left( {\theta_R}\right)}^{4}}}} + {{{3}} {{{\phi_L}}} \cdot {{{{\phi_R}}^{2}}} {{{cos\left( {\theta_R}\right)}^{2}}} {{{sin\left( {\theta_R}\right)}^{2}}}} + {{{{{3}} {{{\phi_L}}} \cdot {{{{\phi_R}}^{2}}} {{{sin\left( {\theta_L}\right)}^{2}}}} - {{{3}} {{{\phi_L}}} \cdot {{{{\phi_R}}^{2}}} {{{sin\left( {\theta_R}\right)}^{2}}}}} - {{{6}} {{{\phi_L}}} \cdot {{{cos\left( {\theta_L}\right)}^{2}}}}} + {{{{6}} {{{\phi_L}}} \cdot {{{cos\left( {\theta_R}\right)}^{2}}}} - {{{9}} {{{\phi_R}}} \cdot {{{{\phi_L}}^{2}}} {{{cos\left( {\theta_L}\right)}^{2}}}}} + {{{3}} {{{\phi_R}}} \cdot {{{{\phi_L}}^{2}}} {{{cos\left( {\theta_L}\right)}^{4}}}} + {{{{3}} {{{\phi_R}}} \cdot {{{{\phi_L}}^{2}}} {{{cos\left( {\theta_L}\right)}^{2}}} {{{sin\left( {\theta_L}\right)}^{2}}}} - {{{3}} {{{\phi_R}}} \cdot {{{{\phi_L}}^{2}}} {{{cos\left( {\theta_R}\right)}^{4}}}}} + {{{{{9}} {{{\phi_R}}} \cdot {{{{\phi_L}}^{2}}} {{{cos\left( {\theta_R}\right)}^{2}}}} - {{{3}} {{{\phi_R}}} \cdot {{{{\phi_L}}^{2}}} {{{cos\left( {\theta_R}\right)}^{2}}} {{{sin\left( {\theta_R}\right)}^{2}}}}} - {{{3}} {{{\phi_R}}} \cdot {{{{\phi_L}}^{2}}} {{{sin\left( {\theta_L}\right)}^{2}}}}} + {{{3}} {{{\phi_R}}} \cdot {{{{\phi_L}}^{2}}} {{{sin\left( {\theta_R}\right)}^{2}}}} + {{{{6}} {{{\phi_R}}} \cdot {{{cos\left( {\theta_L}\right)}^{2}}}} - {{{6}} {{{\phi_R}}} \cdot {{{cos\left( {\theta_R}\right)}^{2}}}}} + {{{{{3}} {{{{\phi_L}}^{3}}} {{{cos\left( {\theta_L}\right)}^{2}}}} - {{{{{\phi_L}}^{3}}} {{{cos\left( {\theta_L}\right)}^{4}}}}} - {{{{{\phi_L}}^{3}}} {{{sin\left( {\theta_L}\right)}^{2}}} {{{cos\left( {\theta_L}\right)}^{2}}}}} + {{{{{{\phi_L}}^{3}}} {{{cos\left( {\theta_R}\right)}^{4}}}} - {{{3}} {{{{\phi_L}}^{3}}} {{{cos\left( {\theta_R}\right)}^{2}}}}} + {{{{{{\phi_L}}^{3}}} {{{sin\left( {\theta_L}\right)}^{2}}}} - {{{{{\phi_L}}^{3}}} {{{sin\left( {\theta_R}\right)}^{2}}}}} + {{{{{{\phi_L}}^{3}}} {{{cos\left( {\theta_R}\right)}^{2}}} {{{sin\left( {\theta_R}\right)}^{2}}}} - {{{3}} {{{{\phi_R}}^{3}}} {{{cos\left( {\theta_L}\right)}^{2}}}}} + {{{{{{{\phi_R}}^{3}}} {{{cos\left( {\theta_L}\right)}^{4}}}} - {{{{{\phi_R}}^{3}}} {{{cos\left( {\theta_R}\right)}^{4}}}}} - {{{{{\phi_R}}^{3}}} {{{sin\left( {\theta_R}\right)}^{2}}} {{{cos\left( {\theta_R}\right)}^{2}}}}} + {{{{3}} {{{{\phi_R}}^{3}}} {{{cos\left( {\theta_R}\right)}^{2}}}} - {{{{{\phi_R}}^{3}}} {{{sin\left( {\theta_L}\right)}^{2}}}}} + {{{{{\phi_R}}^{3}}} {{{cos\left( {\theta_L}\right)}^{2}}} {{{sin\left( {\theta_L}\right)}^{2}}}} + {{{{{\phi_R}}^{3}}} {{{sin\left( {\theta_R}\right)}^{2}}}}})}}}}{{{6}} {{cosh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}}} \\ \frac{{{cos\left( {{{\theta_L}} - {{\theta_R}}}\right)}} {{cosh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}} {{({{{{{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}} \cdot {{cos\left( {\theta_L}\right)}} {{sin\left( {\theta_L}\right)}}} - {{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}} \cdot {{cos\left( {\theta_R}\right)}} {{sin\left( {\theta_R}\right)}}}} - {{{{{\phi_L}}^{2}}} {{sin\left( {\theta_L}\right)}} {{cos\left( {\theta_L}\right)}}}} - {{{{{\phi_R}}^{2}}} {{sin\left( {\theta_L}\right)}} {{cos\left( {\theta_L}\right)}}}} + {{{{{\phi_L}}^{2}}} {{cos\left( {\theta_R}\right)}} {{sin\left( {\theta_R}\right)}}} + {{{{{\phi_R}}^{2}}} {{cos\left( {\theta_R}\right)}} {{sin\left( {\theta_R}\right)}}}})}}}{{{2}} {{w}} {{sinh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}}} & {\frac{1}{2}}{({{{cos\left( {{{\theta_L}} - {{\theta_R}}}\right)}} {{({{{{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}} \cdot {{{cos\left( {\theta_L}\right)}^{2}}}} - {{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}} \cdot {{{cos\left( {\theta_R}\right)}^{2}}}}} - {{{{{\phi_L}}^{2}}} {{{cos\left( {\theta_L}\right)}^{2}}}}} + {{{{{{\phi_L}}^{2}}} {{{cos\left( {\theta_R}\right)}^{2}}}} - {{{{{\phi_R}}^{2}}} {{{cos\left( {\theta_L}\right)}^{2}}}}} + {{{{{\phi_R}}^{2}}} {{{cos\left( {\theta_R}\right)}^{2}}}}})}}})} & {\frac{1}{6}}{({{{cos\left( {{{\theta_L}} - {{\theta_R}}}\right)}} {{({{{{{{{3}} {{{\phi_L}}} \cdot {{{{\phi_R}}^{2}}} {{cos\left( {\theta_L}\right)}} {{sin\left( {\theta_L}\right)}}} - {{{3}} {{{\phi_L}}} \cdot {{{{\phi_R}}^{2}}} {{cos\left( {\theta_R}\right)}} {{sin\left( {\theta_R}\right)}}}} - {{{6}} {{{\phi_L}}} \cdot {{sin\left( {\theta_L}\right)}} {{cos\left( {\theta_L}\right)}}}} - {{{{{\phi_L}}^{3}}} {{sin\left( {\theta_R}\right)}} {{cos\left( {\theta_R}\right)}}}} + {{{6}} {{{\phi_L}}} \cdot {{sin\left( {\theta_R}\right)}} {{cos\left( {\theta_R}\right)}}} + {{{{{{\phi_L}}^{3}}} {{cos\left( {\theta_L}\right)}} {{sin\left( {\theta_L}\right)}}} - {{{3}} {{{\phi_R}}} \cdot {{{{\phi_L}}^{2}}} {{cos\left( {\theta_L}\right)}} {{sin\left( {\theta_L}\right)}}}} + {{{3}} {{{\phi_R}}} \cdot {{{{\phi_L}}^{2}}} {{cos\left( {\theta_R}\right)}} {{sin\left( {\theta_R}\right)}}} + {{{{{6}} {{{\phi_R}}} \cdot {{sin\left( {\theta_L}\right)}} {{cos\left( {\theta_L}\right)}}} - {{{{{\phi_R}}^{3}}} {{sin\left( {\theta_L}\right)}} {{cos\left( {\theta_L}\right)}}}} - {{{6}} {{{\phi_R}}} \cdot {{sin\left( {\theta_R}\right)}} {{cos\left( {\theta_R}\right)}}}} + {{{{{\phi_R}}^{3}}} {{cos\left( {\theta_R}\right)}} {{sin\left( {\theta_R}\right)}}}})}}})} \\ 0 & \frac{-{{{cos\left( {{{\theta_L}} - {{\theta_R}}}\right)}} {{({{{{{3}} {{{\phi_L}}} \cdot {{{{\phi_R}}^{2}}} {{cos\left( {\theta_L}\right)}} {{sin\left( {\theta_R}\right)}}} - {{{3}} {{{\phi_L}}} \cdot {{{{\phi_R}}^{2}}} {{cos\left( {\theta_R}\right)}} {{sin\left( {\theta_L}\right)}}}} + {{{{6}} {{{\phi_L}}} \cdot {{sin\left( {\theta_L}\right)}} {{cos\left( {\theta_R}\right)}}} - {{{6}} {{{\phi_L}}} \cdot {{sin\left( {\theta_R}\right)}} {{cos\left( {\theta_L}\right)}}}} + {{{{{{{\phi_L}}^{3}}} {{cos\left( {\theta_L}\right)}} {{sin\left( {\theta_R}\right)}}} - {{{{{\phi_L}}^{3}}} {{sin\left( {\theta_L}\right)}} {{cos\left( {\theta_R}\right)}}}} - {{{3}} {{{\phi_R}}} \cdot {{{{\phi_L}}^{2}}} {{cos\left( {\theta_L}\right)}} {{sin\left( {\theta_R}\right)}}}} + {{{3}} {{{\phi_R}}} \cdot {{{{\phi_L}}^{2}}} {{cos\left( {\theta_R}\right)}} {{sin\left( {\theta_L}\right)}}} + {{{{{{\phi_R}}^{3}}} {{cos\left( {\theta_R}\right)}} {{sin\left( {\theta_L}\right)}}} - {{{6}} {{{\phi_R}}} \cdot {{sin\left( {\theta_L}\right)}} {{cos\left( {\theta_R}\right)}}}} + {{{{6}} {{{\phi_R}}} \cdot {{sin\left( {\theta_R}\right)}} {{cos\left( {\theta_L}\right)}}} - {{{{{\phi_R}}^{3}}} {{sin\left( {\theta_R}\right)}} {{cos\left( {\theta_L}\right)}}}}})}}}}{{{6}} {{sin\left( {\theta_R}\right)}} {{sin\left( {\theta_L}\right)}}} & 0\end{matrix}\right] & 0 \\ 0 & 0 & \left[\begin{matrix} \frac{-{{{|{sin\left( {\theta_L}\right)}|}} {{({{{{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}} \cdot {{{cos\left( {\theta_L}\right)}^{2}}}} - {{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}} \cdot {{{cos\left( {\theta_R}\right)}^{2}}}}} - {{{{{\phi_L}}^{2}}} {{{cos\left( {\theta_L}\right)}^{2}}}}} + {{{{{{\phi_L}}^{2}}} {{{cos\left( {\theta_R}\right)}^{2}}}} - {{{{{\phi_R}}^{2}}} {{{cos\left( {\theta_L}\right)}^{2}}}}} + {{{{{\phi_R}}^{2}}} {{{cos\left( {\theta_R}\right)}^{2}}}}})}}}}{{{2}} {{|{sin\left( {\theta_R}\right)}|}}} & \frac{{{w}} {{|{sin\left( {\theta_L}\right)}|}} {{sinh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}} {{({{{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}} \cdot {{cos\left( {\theta_L}\right)}} {{sin\left( {\theta_L}\right)}}} - {{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}} \cdot {{cos\left( {\theta_R}\right)}} {{sin\left( {\theta_R}\right)}}}} + {{{{{{\phi_L}}^{2}}} {{cos\left( {\theta_R}\right)}} {{sin\left( {\theta_R}\right)}}} - {{{{{\phi_L}}^{2}}} {{sin\left( {\theta_L}\right)}} {{cos\left( {\theta_L}\right)}}}} + {{{{{{\phi_R}}^{2}}} {{cos\left( {\theta_R}\right)}} {{sin\left( {\theta_R}\right)}}} - {{{{{\phi_R}}^{2}}} {{sin\left( {\theta_L}\right)}} {{cos\left( {\theta_L}\right)}}}}})}}}{{{2}} {{cosh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}} {{|{sin\left( {\theta_R}\right)}|}}} & \frac{-{{{w}} {{|{sin\left( {\theta_L}\right)}|}} {{sinh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}} {{({{{{{{{9}} {{{\phi_L}}} \cdot {{{{\phi_R}}^{2}}} {{{cos\left( {\theta_L}\right)}^{2}}}} - {{{3}} {{{\phi_L}}} \cdot {{{{\phi_R}}^{2}}} {{{cos\left( {\theta_L}\right)}^{4}}}}} - {{{3}} {{{\phi_L}}} \cdot {{{{\phi_R}}^{2}}} {{{cos\left( {\theta_L}\right)}^{2}}} {{{sin\left( {\theta_L}\right)}^{2}}}}} - {{{9}} {{{\phi_L}}} \cdot {{{{\phi_R}}^{2}}} {{{cos\left( {\theta_R}\right)}^{2}}}}} + {{{3}} {{{\phi_L}}} \cdot {{{{\phi_R}}^{2}}} {{{cos\left( {\theta_R}\right)}^{4}}}} + {{{3}} {{{\phi_L}}} \cdot {{{{\phi_R}}^{2}}} {{{cos\left( {\theta_R}\right)}^{2}}} {{{sin\left( {\theta_R}\right)}^{2}}}} + {{{{{3}} {{{\phi_L}}} \cdot {{{{\phi_R}}^{2}}} {{{sin\left( {\theta_L}\right)}^{2}}}} - {{{3}} {{{\phi_L}}} \cdot {{{{\phi_R}}^{2}}} {{{sin\left( {\theta_R}\right)}^{2}}}}} - {{{6}} {{{\phi_L}}} \cdot {{{cos\left( {\theta_L}\right)}^{2}}}}} + {{{{6}} {{{\phi_L}}} \cdot {{{cos\left( {\theta_R}\right)}^{2}}}} - {{{9}} {{{\phi_R}}} \cdot {{{{\phi_L}}^{2}}} {{{cos\left( {\theta_L}\right)}^{2}}}}} + {{{3}} {{{\phi_R}}} \cdot {{{{\phi_L}}^{2}}} {{{cos\left( {\theta_L}\right)}^{4}}}} + {{{{3}} {{{\phi_R}}} \cdot {{{{\phi_L}}^{2}}} {{{cos\left( {\theta_L}\right)}^{2}}} {{{sin\left( {\theta_L}\right)}^{2}}}} - {{{3}} {{{\phi_R}}} \cdot {{{{\phi_L}}^{2}}} {{{cos\left( {\theta_R}\right)}^{4}}}}} + {{{{{9}} {{{\phi_R}}} \cdot {{{{\phi_L}}^{2}}} {{{cos\left( {\theta_R}\right)}^{2}}}} - {{{3}} {{{\phi_R}}} \cdot {{{{\phi_L}}^{2}}} {{{cos\left( {\theta_R}\right)}^{2}}} {{{sin\left( {\theta_R}\right)}^{2}}}}} - {{{3}} {{{\phi_R}}} \cdot {{{{\phi_L}}^{2}}} {{{sin\left( {\theta_L}\right)}^{2}}}}} + {{{3}} {{{\phi_R}}} \cdot {{{{\phi_L}}^{2}}} {{{sin\left( {\theta_R}\right)}^{2}}}} + {{{{6}} {{{\phi_R}}} \cdot {{{cos\left( {\theta_L}\right)}^{2}}}} - {{{6}} {{{\phi_R}}} \cdot {{{cos\left( {\theta_R}\right)}^{2}}}}} + {{{{{3}} {{{{\phi_L}}^{3}}} {{{cos\left( {\theta_L}\right)}^{2}}}} - {{{{{\phi_L}}^{3}}} {{{cos\left( {\theta_L}\right)}^{4}}}}} - {{{{{\phi_L}}^{3}}} {{{sin\left( {\theta_L}\right)}^{2}}} {{{cos\left( {\theta_L}\right)}^{2}}}}} + {{{{{{\phi_L}}^{3}}} {{{cos\left( {\theta_R}\right)}^{4}}}} - {{{3}} {{{{\phi_L}}^{3}}} {{{cos\left( {\theta_R}\right)}^{2}}}}} + {{{{{{\phi_L}}^{3}}} {{{sin\left( {\theta_L}\right)}^{2}}}} - {{{{{\phi_L}}^{3}}} {{{sin\left( {\theta_R}\right)}^{2}}}}} + {{{{{{\phi_L}}^{3}}} {{{cos\left( {\theta_R}\right)}^{2}}} {{{sin\left( {\theta_R}\right)}^{2}}}} - {{{3}} {{{{\phi_R}}^{3}}} {{{cos\left( {\theta_L}\right)}^{2}}}}} + {{{{{{{\phi_R}}^{3}}} {{{cos\left( {\theta_L}\right)}^{4}}}} - {{{{{\phi_R}}^{3}}} {{{cos\left( {\theta_R}\right)}^{4}}}}} - {{{{{\phi_R}}^{3}}} {{{sin\left( {\theta_R}\right)}^{2}}} {{{cos\left( {\theta_R}\right)}^{2}}}}} + {{{{3}} {{{{\phi_R}}^{3}}} {{{cos\left( {\theta_R}\right)}^{2}}}} - {{{{{\phi_R}}^{3}}} {{{sin\left( {\theta_L}\right)}^{2}}}}} + {{{{{\phi_R}}^{3}}} {{{cos\left( {\theta_L}\right)}^{2}}} {{{sin\left( {\theta_L}\right)}^{2}}}} + {{{{{\phi_R}}^{3}}} {{{sin\left( {\theta_R}\right)}^{2}}}}})}}}}{{{6}} {{cosh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}} {{|{sin\left( {\theta_R}\right)}|}}} \\ \frac{{{|{sin\left( {\theta_L}\right)}|}} {{cosh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}} {{({{{{{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}} \cdot {{cos\left( {\theta_L}\right)}} {{sin\left( {\theta_L}\right)}}} - {{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}} \cdot {{cos\left( {\theta_R}\right)}} {{sin\left( {\theta_R}\right)}}}} - {{{{{\phi_L}}^{2}}} {{sin\left( {\theta_L}\right)}} {{cos\left( {\theta_L}\right)}}}} - {{{{{\phi_R}}^{2}}} {{sin\left( {\theta_L}\right)}} {{cos\left( {\theta_L}\right)}}}} + {{{{{\phi_L}}^{2}}} {{cos\left( {\theta_R}\right)}} {{sin\left( {\theta_R}\right)}}} + {{{{{\phi_R}}^{2}}} {{cos\left( {\theta_R}\right)}} {{sin\left( {\theta_R}\right)}}}})}}}{{{2}} {{w}} {{sinh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}} {{|{sin\left( {\theta_R}\right)}|}}} & \frac{{{|{sin\left( {\theta_L}\right)}|}} {{({{{{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}} \cdot {{{cos\left( {\theta_L}\right)}^{2}}}} - {{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}} \cdot {{{cos\left( {\theta_R}\right)}^{2}}}}} - {{{{{\phi_L}}^{2}}} {{{cos\left( {\theta_L}\right)}^{2}}}}} + {{{{{{\phi_L}}^{2}}} {{{cos\left( {\theta_R}\right)}^{2}}}} - {{{{{\phi_R}}^{2}}} {{{cos\left( {\theta_L}\right)}^{2}}}}} + {{{{{\phi_R}}^{2}}} {{{cos\left( {\theta_R}\right)}^{2}}}}})}}}{{{2}} {{|{sin\left( {\theta_R}\right)}|}}} & \frac{{{|{sin\left( {\theta_L}\right)}|}} {{({{{{{{3}} {{{\phi_L}}} \cdot {{{{\phi_R}}^{2}}} {{cos\left( {\theta_L}\right)}} {{sin\left( {\theta_L}\right)}}} - {{{3}} {{{\phi_L}}} \cdot {{{{\phi_R}}^{2}}} {{cos\left( {\theta_R}\right)}} {{sin\left( {\theta_R}\right)}}}} - {{{6}} {{{\phi_L}}} \cdot {{sin\left( {\theta_L}\right)}} {{cos\left( {\theta_L}\right)}}}} + {{{{6}} {{{\phi_L}}} \cdot {{sin\left( {\theta_R}\right)}} {{cos\left( {\theta_R}\right)}}} - {{{{{\phi_L}}^{3}}} {{sin\left( {\theta_R}\right)}} {{cos\left( {\theta_R}\right)}}}} + {{{{{{\phi_L}}^{3}}} {{cos\left( {\theta_L}\right)}} {{sin\left( {\theta_L}\right)}}} - {{{3}} {{{\phi_R}}} \cdot {{{{\phi_L}}^{2}}} {{cos\left( {\theta_L}\right)}} {{sin\left( {\theta_L}\right)}}}} + {{{{3}} {{{\phi_R}}} \cdot {{{{\phi_L}}^{2}}} {{cos\left( {\theta_R}\right)}} {{sin\left( {\theta_R}\right)}}} - {{{{{\phi_R}}^{3}}} {{sin\left( {\theta_L}\right)}} {{cos\left( {\theta_L}\right)}}}} + {{{{6}} {{{\phi_R}}} \cdot {{sin\left( {\theta_L}\right)}} {{cos\left( {\theta_L}\right)}}} - {{{6}} {{{\phi_R}}} \cdot {{sin\left( {\theta_R}\right)}} {{cos\left( {\theta_R}\right)}}}} + {{{{{\phi_R}}^{3}}} {{cos\left( {\theta_R}\right)}} {{sin\left( {\theta_R}\right)}}}})}}}{{{6}} {{|{sin\left( {\theta_R}\right)}|}}} \\ 0 & \frac{-{{{|{sin\left( {\theta_L}\right)}|}} {{({{{{{3}} {{{\phi_L}}} \cdot {{{{\phi_R}}^{2}}} {{cos\left( {\theta_L}\right)}} {{sin\left( {\theta_R}\right)}}} - {{{3}} {{{\phi_L}}} \cdot {{{{\phi_R}}^{2}}} {{cos\left( {\theta_R}\right)}} {{sin\left( {\theta_L}\right)}}}} + {{{{6}} {{{\phi_L}}} \cdot {{sin\left( {\theta_L}\right)}} {{cos\left( {\theta_R}\right)}}} - {{{6}} {{{\phi_L}}} \cdot {{sin\left( {\theta_R}\right)}} {{cos\left( {\theta_L}\right)}}}} + {{{{{{{\phi_L}}^{3}}} {{cos\left( {\theta_L}\right)}} {{sin\left( {\theta_R}\right)}}} - {{{{{\phi_L}}^{3}}} {{sin\left( {\theta_L}\right)}} {{cos\left( {\theta_R}\right)}}}} - {{{3}} {{{\phi_R}}} \cdot {{{{\phi_L}}^{2}}} {{cos\left( {\theta_L}\right)}} {{sin\left( {\theta_R}\right)}}}} + {{{{3}} {{{\phi_R}}} \cdot {{{{\phi_L}}^{2}}} {{cos\left( {\theta_R}\right)}} {{sin\left( {\theta_L}\right)}}} - {{{6}} {{{\phi_R}}} \cdot {{sin\left( {\theta_L}\right)}} {{cos\left( {\theta_R}\right)}}}} + {{{{{\phi_R}}^{3}}} {{cos\left( {\theta_R}\right)}} {{sin\left( {\theta_L}\right)}}} + {{{{6}} {{{\phi_R}}} \cdot {{sin\left( {\theta_R}\right)}} {{cos\left( {\theta_L}\right)}}} - {{{{{\phi_R}}^{3}}} {{sin\left( {\theta_R}\right)}} {{cos\left( {\theta_L}\right)}}}}})}}}}{{{6}} {{sin\left( {\theta_L}\right)}} {{sin\left( {\theta_R}\right)}} {{|{sin\left( {\theta_R}\right)}|}}} & 0\end{matrix}\right]\end{matrix}\right]$
propagator partials
${{\frac{\partial}{\partial \rho}}\left( \left[\begin{matrix} \frac{cosh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}{cosh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)} & 0 & 0 \\ 0 & \frac{|{sinh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}|}{|{sinh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)}|} & 0 \\ 0 & 0 & \frac{|{sinh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}|}{|{sinh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)}|}\end{matrix}\right]\right)} = {\left[\begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix}\right]}$
${{\frac{\partial}{\partial \theta}}\left( \left[\begin{matrix} \frac{cosh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}{cosh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)} & 0 & 0 \\ 0 & \frac{|{sinh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}|}{|{sinh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)}|} & 0 \\ 0 & 0 & \frac{|{sinh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}|}{|{sinh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)}|}\end{matrix}\right]\right)} = {\left[\begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix}\right]}$
${{\frac{\partial}{\partial \phi}}\left( \left[\begin{matrix} \frac{cosh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}{cosh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)} & 0 & 0 \\ 0 & \frac{|{sinh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}|}{|{sinh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)}|} & 0 \\ 0 & 0 & \frac{|{sinh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}|}{|{sinh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)}|}\end{matrix}\right]\right)} = {\left[\begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix}\right]}$
${{\frac{\partial}{\partial \rho}}\left( \left[\begin{matrix} cos\left( {{{\theta_L}} - {{\theta_R}}}\right) & \frac{-{{{w}} {{sin\left( {{{\theta_L}} - {{\theta_R}}}\right)}} {{sinh\left( {{\frac{1}{w}}{({\rho})}}\right)}}}}{cosh\left( {{\frac{1}{w}}{({\rho})}}\right)} & 0 \\ \frac{{{cosh\left( {{\frac{1}{w}}{({\rho})}}\right)}} {{sin\left( {{{\theta_L}} - {{\theta_R}}}\right)}}}{{{w}} {{sinh\left( {{\frac{1}{w}}{({\rho})}}\right)}}} & cos\left( {{{\theta_L}} - {{\theta_R}}}\right) & 0 \\ 0 & 0 & \frac{|{sin\left( {\theta_L}\right)}|}{|{sin\left( {\theta_R}\right)}|}\end{matrix}\right]\right)} = {\left[\begin{matrix} 0 & \frac{-{{{sin\left( {{{\theta_L}} - {{\theta_R}}}\right)}} {{({{{cosh\left( {{\frac{1}{w}}{({\rho})}}\right)}^{2}} - {{sinh\left( {{\frac{1}{w}}{({\rho})}}\right)}^{2}}})}}}}{{cosh\left( {{\frac{1}{w}}{({\rho})}}\right)}^{2}} & 0 \\ \frac{-{{{sin\left( {{{\theta_L}} - {{\theta_R}}}\right)}} {{({{{cosh\left( {{\frac{1}{w}}{({\rho})}}\right)}^{2}} - {{sinh\left( {{\frac{1}{w}}{({\rho})}}\right)}^{2}}})}}}}{{{{w}^{2}}} {{{sinh\left( {{\frac{1}{w}}{({\rho})}}\right)}^{2}}}} & 0 & 0 \\ 0 & 0 & 0\end{matrix}\right]}$
${{\frac{\partial}{\partial \theta}}\left( \left[\begin{matrix} cos\left( {{{\theta_L}} - {{\theta_R}}}\right) & \frac{-{{{w}} {{sin\left( {{{\theta_L}} - {{\theta_R}}}\right)}} {{sinh\left( {{\frac{1}{w}}{({\rho})}}\right)}}}}{cosh\left( {{\frac{1}{w}}{({\rho})}}\right)} & 0 \\ \frac{{{cosh\left( {{\frac{1}{w}}{({\rho})}}\right)}} {{sin\left( {{{\theta_L}} - {{\theta_R}}}\right)}}}{{{w}} {{sinh\left( {{\frac{1}{w}}{({\rho})}}\right)}}} & cos\left( {{{\theta_L}} - {{\theta_R}}}\right) & 0 \\ 0 & 0 & \frac{|{sin\left( {\theta_L}\right)}|}{|{sin\left( {\theta_R}\right)}|}\end{matrix}\right]\right)} = {\left[\begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix}\right]}$
${{\frac{\partial}{\partial \phi}}\left( \left[\begin{matrix} cos\left( {{{\theta_L}} - {{\theta_R}}}\right) & \frac{-{{{w}} {{sin\left( {{{\theta_L}} - {{\theta_R}}}\right)}} {{sinh\left( {{\frac{1}{w}}{({\rho})}}\right)}}}}{cosh\left( {{\frac{1}{w}}{({\rho})}}\right)} & 0 \\ \frac{{{cosh\left( {{\frac{1}{w}}{({\rho})}}\right)}} {{sin\left( {{{\theta_L}} - {{\theta_R}}}\right)}}}{{{w}} {{sinh\left( {{\frac{1}{w}}{({\rho})}}\right)}}} & cos\left( {{{\theta_L}} - {{\theta_R}}}\right) & 0 \\ 0 & 0 & \frac{|{sin\left( {\theta_L}\right)}|}{|{sin\left( {\theta_R}\right)}|}\end{matrix}\right]\right)} = {\left[\begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix}\right]}$
${{\frac{\partial}{\partial \rho}}\left({{\left[\begin{matrix} {\frac{1}{2}}{({-{({{{{{\phi_L}}^{2}} - {{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}} \cdot {{{cos\left( \theta\right)}^{2}}}} - {{{{{\phi_L}}^{2}}} {{{cos\left( \theta\right)}^{2}}}}} + {{{{\phi_R}}^{2}} - {{{{{\phi_R}}^{2}}} {{{cos\left( \theta\right)}^{2}}}}}})}})} & \frac{{{w}} {{({{{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_L}}^{2}}} - {{{\phi_R}}^{2}}})}} {{sin\left( \theta\right)}} {{cos\left( \theta\right)}} {{sinh\left( {{\frac{1}{w}}{({\rho})}}\right)}}}{{{2}} {{cosh\left( {{\frac{1}{w}}{({\rho})}}\right)}}} & \frac{{{w}} {{sinh\left( {{\frac{1}{w}}{({\rho})}}\right)}} {{({{{{{3}} {{{\phi_L}}} \cdot {{{{\phi_R}}^{2}}} {{{cos\left( \theta\right)}^{4}}}} - {{{9}} {{{\phi_L}}} \cdot {{{{\phi_R}}^{2}}} {{{cos\left( \theta\right)}^{2}}}}} + {{{{3}} {{{\phi_L}}} \cdot {{{{\phi_R}}^{2}}} {{{cos\left( \theta\right)}^{2}}} {{{sin\left( \theta\right)}^{2}}}} - {{{3}} {{{\phi_L}}} \cdot {{{{\phi_R}}^{2}}} {{{sin\left( \theta\right)}^{2}}}}} + {{{6}} {{{\phi_L}}} \cdot {{{{\phi_R}}^{2}}}} + {{{{{6}} {{{\phi_L}}} \cdot {{{cos\left( \theta\right)}^{2}}}} - {{{6}} {{{\phi_L}}}}} - {{{3}} {{{\phi_R}}} \cdot {{{{\phi_L}}^{2}}} {{{cos\left( \theta\right)}^{4}}}}} + {{{{9}} {{{\phi_R}}} \cdot {{{{\phi_L}}^{2}}} {{{cos\left( \theta\right)}^{2}}}} - {{{3}} {{{\phi_R}}} \cdot {{{{\phi_L}}^{2}}} {{{cos\left( \theta\right)}^{2}}} {{{sin\left( \theta\right)}^{2}}}}} + {{{{{3}} {{{\phi_R}}} \cdot {{{{\phi_L}}^{2}}} {{{sin\left( \theta\right)}^{2}}}} - {{{6}} {{{\phi_R}}} \cdot {{{{\phi_L}}^{2}}}}} - {{{6}} {{{\phi_R}}} \cdot {{{cos\left( \theta\right)}^{2}}}}} + {{{6}} {{{\phi_R}}}} + {{{{{\phi_L}}^{3}}} {{{cos\left( \theta\right)}^{2}}} {{{sin\left( \theta\right)}^{2}}}} + {{{{{{{\phi_L}}^{3}}} {{{cos\left( \theta\right)}^{4}}}} - {{{3}} {{{{\phi_L}}^{3}}} {{{cos\left( \theta\right)}^{2}}}}} - {{{{{\phi_L}}^{3}}} {{{sin\left( \theta\right)}^{2}}}}} + {{{2}} {{{{\phi_L}}^{3}}}} + {{{{{3}} {{{{\phi_R}}^{3}}} {{{cos\left( \theta\right)}^{2}}}} - {{{{{\phi_R}}^{3}}} {{{cos\left( \theta\right)}^{4}}}}} - {{{{{\phi_R}}^{3}}} {{{sin\left( \theta\right)}^{2}}} {{{cos\left( \theta\right)}^{2}}}}} + {{{{{{\phi_R}}^{3}}} {{{sin\left( \theta\right)}^{2}}}} - {{{2}} {{{{\phi_R}}^{3}}}}}})}}}{{{6}} {{cosh\left( {{\frac{1}{w}}{({\rho})}}\right)}}} \\ \frac{-{{{{({{{\phi_L}} - {{\phi_R}}})}^{2}}} {{sin\left( \theta\right)}} {{cos\left( \theta\right)}} {{cosh\left( {{\frac{1}{w}}{({\rho})}}\right)}}}}{{{2}} {{w}} {{sinh\left( {{\frac{1}{w}}{({\rho})}}\right)}}} & {\frac{1}{2}}{({{{{cos\left( \theta\right)}^{2}}} {{({{{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_L}}^{2}}} - {{{\phi_R}}^{2}}})}}})} & {\frac{1}{6}}{({{{sin\left( \theta\right)}} {{cos\left( \theta\right)}} {{({{{{{{3}} {{{\phi_L}}} \cdot {{{{\phi_R}}^{2}}}} - {{{6}} {{{\phi_L}}}}} - {{{3}} {{{\phi_R}}} \cdot {{{{\phi_L}}^{2}}}}} + {{{{6}} {{{\phi_R}}}} - {{{\phi_R}}^{3}}} + {{{\phi_L}}^{3}}})}}})} \\ \frac{-{{{cosh\left( {{\frac{1}{w}}{({\rho})}}\right)}} {{({{{{3}} {{{\phi_L}}} \cdot {{{{\phi_R}}^{2}}}} + {{{{{\phi_L}}^{3}} - {{{6}} {{{\phi_L}}}}} - {{{3}} {{{\phi_R}}} \cdot {{{{\phi_L}}^{2}}}}} + {{{{6}} {{{\phi_R}}}} - {{{\phi_R}}^{3}}}})}}}}{{{6}} {{w}} {{sinh\left( {{\frac{1}{w}}{({\rho})}}\right)}}} & \frac{-{{{cos\left( \theta\right)}} {{({{{{3}} {{{\phi_L}}} \cdot {{{{\phi_R}}^{2}}}} + {{{{{\phi_L}}^{3}} - {{{6}} {{{\phi_L}}}}} - {{{3}} {{{\phi_R}}} \cdot {{{{\phi_L}}^{2}}}}} + {{{{6}} {{{\phi_R}}}} - {{{\phi_R}}^{3}}}})}}}}{{{6}} {{sin\left( \theta\right)}}} & {\frac{1}{2}}{({-{({{{{{\phi_L}}^{2}} - {{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}}} + {{{\phi_R}}^{2}}})}})}\end{matrix}\right]} + {{\mathcal{O}(A^4)}}}\right)} = {\left[\begin{matrix} 0 & \frac{{{cos\left( \theta\right)}} {{sin\left( \theta\right)}} {{({{{{{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}} \cdot {{{cosh\left( {{\frac{1}{w}}{({\rho})}}\right)}^{2}}}} - {{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}} \cdot {{{sinh\left( {{\frac{1}{w}}{({\rho})}}\right)}^{2}}}}} - {{{{{\phi_L}}^{2}}} {{{cosh\left( {{\frac{1}{w}}{({\rho})}}\right)}^{2}}}}} - {{{{{\phi_R}}^{2}}} {{{cosh\left( {{\frac{1}{w}}{({\rho})}}\right)}^{2}}}}} + {{{{{\phi_L}}^{2}}} {{{sinh\left( {{\frac{1}{w}}{({\rho})}}\right)}^{2}}}} + {{{{{\phi_R}}^{2}}} {{{sinh\left( {{\frac{1}{w}}{({\rho})}}\right)}^{2}}}}})}}}{{{2}} {{{cosh\left( {{\frac{1}{w}}{({\rho})}}\right)}^{2}}}} & \frac{-{({{{{{{9}} {{{\phi_L}}} \cdot {{{{\phi_R}}^{2}}} {{{cos\left( \theta\right)}^{2}}} {{{cosh\left( {{\frac{1}{w}}{({\rho})}}\right)}^{2}}}} - {{{3}} {{{\phi_L}}} \cdot {{{{\phi_R}}^{2}}} {{{sin\left( \theta\right)}^{2}}} {{{cos\left( \theta\right)}^{2}}} {{{cosh\left( {{\frac{1}{w}}{({\rho})}}\right)}^{2}}}}} - {{{9}} {{{\phi_L}}} \cdot {{{{\phi_R}}^{2}}} {{{cos\left( \theta\right)}^{2}}} {{{sinh\left( {{\frac{1}{w}}{({\rho})}}\right)}^{2}}}}} + {{{{{3}} {{{\phi_L}}} \cdot {{{{\phi_R}}^{2}}} {{{sin\left( \theta\right)}^{2}}} {{{cos\left( \theta\right)}^{2}}} {{{sinh\left( {{\frac{1}{w}}{({\rho})}}\right)}^{2}}}} - {{{6}} {{{\phi_L}}} \cdot {{{{\phi_R}}^{2}}} {{{cosh\left( {{\frac{1}{w}}{({\rho})}}\right)}^{2}}}}} - {{{3}} {{{\phi_L}}} \cdot {{{{\phi_R}}^{2}}} {{{cosh\left( {{\frac{1}{w}}{({\rho})}}\right)}^{2}}} {{{cos\left( \theta\right)}^{4}}}}} + {{{3}} {{{\phi_L}}} \cdot {{{{\phi_R}}^{2}}} {{{sin\left( \theta\right)}^{2}}} {{{cosh\left( {{\frac{1}{w}}{({\rho})}}\right)}^{2}}}} + {{{6}} {{{\phi_L}}} \cdot {{{{\phi_R}}^{2}}} {{{sinh\left( {{\frac{1}{w}}{({\rho})}}\right)}^{2}}}} + {{{{3}} {{{\phi_L}}} \cdot {{{{\phi_R}}^{2}}} {{{sinh\left( {{\frac{1}{w}}{({\rho})}}\right)}^{2}}} {{{cos\left( \theta\right)}^{4}}}} - {{{3}} {{{\phi_L}}} \cdot {{{{\phi_R}}^{2}}} {{{sin\left( \theta\right)}^{2}}} {{{sinh\left( {{\frac{1}{w}}{({\rho})}}\right)}^{2}}}}} + {{{{3}} {{{{\phi_L}}^{3}}} {{{cosh\left( {{\frac{1}{w}}{({\rho})}}\right)}^{2}}} {{{cos\left( \theta\right)}^{2}}}} - {{{6}} {{{\phi_L}}} \cdot {{{cosh\left( {{\frac{1}{w}}{({\rho})}}\right)}^{2}}} {{{cos\left( \theta\right)}^{2}}}}} + {{{{6}} {{{\phi_L}}} \cdot {{{sinh\left( {{\frac{1}{w}}{({\rho})}}\right)}^{2}}} {{{cos\left( \theta\right)}^{2}}}} - {{{3}} {{{{\phi_L}}^{3}}} {{{sinh\left( {{\frac{1}{w}}{({\rho})}}\right)}^{2}}} {{{cos\left( \theta\right)}^{2}}}}} + {{{{{6}} {{{\phi_L}}} \cdot {{{cosh\left( {{\frac{1}{w}}{({\rho})}}\right)}^{2}}}} - {{{2}} {{{{\phi_L}}^{3}}} {{{cosh\left( {{\frac{1}{w}}{({\rho})}}\right)}^{2}}}}} - {{{{{\phi_L}}^{3}}} {{{cosh\left( {{\frac{1}{w}}{({\rho})}}\right)}^{2}}} {{{cos\left( \theta\right)}^{4}}}}} + {{{{{{\phi_L}}^{3}}} {{{sin\left( \theta\right)}^{2}}} {{{cosh\left( {{\frac{1}{w}}{({\rho})}}\right)}^{2}}}} - {{{{{\phi_L}}^{3}}} {{{cos\left( \theta\right)}^{2}}} {{{cosh\left( {{\frac{1}{w}}{({\rho})}}\right)}^{2}}} {{{sin\left( \theta\right)}^{2}}}}} + {{{{{{{\phi_L}}^{3}}} {{{sinh\left( {{\frac{1}{w}}{({\rho})}}\right)}^{2}}} {{{sin\left( \theta\right)}^{2}}} {{{cos\left( \theta\right)}^{2}}}} - {{{{{\phi_L}}^{3}}} {{{sinh\left( {{\frac{1}{w}}{({\rho})}}\right)}^{2}}} {{{sin\left( \theta\right)}^{2}}}}} - {{{6}} {{{\phi_L}}} \cdot {{{sinh\left( {{\frac{1}{w}}{({\rho})}}\right)}^{2}}}}} + {{{2}} {{{{\phi_L}}^{3}}} {{{sinh\left( {{\frac{1}{w}}{({\rho})}}\right)}^{2}}}} + {{{{{{\phi_L}}^{3}}} {{{sinh\left( {{\frac{1}{w}}{({\rho})}}\right)}^{2}}} {{{cos\left( \theta\right)}^{4}}}} - {{{9}} {{{\phi_R}}} \cdot {{{{\phi_L}}^{2}}} {{{cos\left( \theta\right)}^{2}}} {{{cosh\left( {{\frac{1}{w}}{({\rho})}}\right)}^{2}}}}} + {{{3}} {{{\phi_R}}} \cdot {{{{\phi_L}}^{2}}} {{{sin\left( \theta\right)}^{2}}} {{{cos\left( \theta\right)}^{2}}} {{{cosh\left( {{\frac{1}{w}}{({\rho})}}\right)}^{2}}}} + {{{{9}} {{{\phi_R}}} \cdot {{{{\phi_L}}^{2}}} {{{cos\left( \theta\right)}^{2}}} {{{sinh\left( {{\frac{1}{w}}{({\rho})}}\right)}^{2}}}} - {{{3}} {{{\phi_R}}} \cdot {{{{\phi_L}}^{2}}} {{{sin\left( \theta\right)}^{2}}} {{{cos\left( \theta\right)}^{2}}} {{{sinh\left( {{\frac{1}{w}}{({\rho})}}\right)}^{2}}}}} + {{{6}} {{{\phi_R}}} \cdot {{{{\phi_L}}^{2}}} {{{cosh\left( {{\frac{1}{w}}{({\rho})}}\right)}^{2}}}} + {{{{{{3}} {{{\phi_R}}} \cdot {{{{\phi_L}}^{2}}} {{{cosh\left( {{\frac{1}{w}}{({\rho})}}\right)}^{2}}} {{{cos\left( \theta\right)}^{4}}}} - {{{3}} {{{\phi_R}}} \cdot {{{{\phi_L}}^{2}}} {{{sin\left( \theta\right)}^{2}}} {{{cosh\left( {{\frac{1}{w}}{({\rho})}}\right)}^{2}}}}} - {{{6}} {{{\phi_R}}} \cdot {{{{\phi_L}}^{2}}} {{{sinh\left( {{\frac{1}{w}}{({\rho})}}\right)}^{2}}}}} - {{{3}} {{{\phi_R}}} \cdot {{{{\phi_L}}^{2}}} {{{sinh\left( {{\frac{1}{w}}{({\rho})}}\right)}^{2}}} {{{cos\left( \theta\right)}^{4}}}}} + {{{3}} {{{\phi_R}}} \cdot {{{{\phi_L}}^{2}}} {{{sin\left( \theta\right)}^{2}}} {{{sinh\left( {{\frac{1}{w}}{({\rho})}}\right)}^{2}}}} + {{{{{6}} {{{\phi_R}}} \cdot {{{cosh\left( {{\frac{1}{w}}{({\rho})}}\right)}^{2}}} {{{cos\left( \theta\right)}^{2}}}} - {{{3}} {{{{\phi_R}}^{3}}} {{{cosh\left( {{\frac{1}{w}}{({\rho})}}\right)}^{2}}} {{{cos\left( \theta\right)}^{2}}}}} - {{{6}} {{{\phi_R}}} \cdot {{{sinh\left( {{\frac{1}{w}}{({\rho})}}\right)}^{2}}} {{{cos\left( \theta\right)}^{2}}}}} + {{{{3}} {{{{\phi_R}}^{3}}} {{{sinh\left( {{\frac{1}{w}}{({\rho})}}\right)}^{2}}} {{{cos\left( \theta\right)}^{2}}}} - {{{6}} {{{\phi_R}}} \cdot {{{cosh\left( {{\frac{1}{w}}{({\rho})}}\right)}^{2}}}}} + {{{2}} {{{{\phi_R}}^{3}}} {{{cosh\left( {{\frac{1}{w}}{({\rho})}}\right)}^{2}}}} + {{{{{\phi_R}}^{3}}} {{{cosh\left( {{\frac{1}{w}}{({\rho})}}\right)}^{2}}} {{{cos\left( \theta\right)}^{4}}}} + {{{{{{\phi_R}}^{3}}} {{{cosh\left( {{\frac{1}{w}}{({\rho})}}\right)}^{2}}} {{{sin\left( \theta\right)}^{2}}} {{{cos\left( \theta\right)}^{2}}}} - {{{{{\phi_R}}^{3}}} {{{cosh\left( {{\frac{1}{w}}{({\rho})}}\right)}^{2}}} {{{sin\left( \theta\right)}^{2}}}}} + {{{{{6}} {{{\phi_R}}} \cdot {{{sinh\left( {{\frac{1}{w}}{({\rho})}}\right)}^{2}}}} - {{{2}} {{{{\phi_R}}^{3}}} {{{sinh\left( {{\frac{1}{w}}{({\rho})}}\right)}^{2}}}}} - {{{{{\phi_R}}^{3}}} {{{sinh\left( {{\frac{1}{w}}{({\rho})}}\right)}^{2}}} {{{cos\left( \theta\right)}^{4}}}}} + {{{{{{\phi_R}}^{3}}} {{{sin\left( \theta\right)}^{2}}} {{{sinh\left( {{\frac{1}{w}}{({\rho})}}\right)}^{2}}}} - {{{{{\phi_R}}^{3}}} {{{cos\left( \theta\right)}^{2}}} {{{sinh\left( {{\frac{1}{w}}{({\rho})}}\right)}^{2}}} {{{sin\left( \theta\right)}^{2}}}}}})}}{{{6}} {{{cosh\left( {{\frac{1}{w}}{({\rho})}}\right)}^{2}}}} \\ \frac{-{{{cos\left( \theta\right)}} {{sin\left( \theta\right)}} {{({{{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}} \cdot {{{cosh\left( {{\frac{1}{w}}{({\rho})}}\right)}^{2}}}} - {{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}} \cdot {{{sinh\left( {{\frac{1}{w}}{({\rho})}}\right)}^{2}}}}} + {{{{{\phi_L}}^{2}}} {{{sinh\left( {{\frac{1}{w}}{({\rho})}}\right)}^{2}}}} + {{{{{{{\phi_R}}^{2}}} {{{sinh\left( {{\frac{1}{w}}{({\rho})}}\right)}^{2}}}} - {{{{{\phi_L}}^{2}}} {{{cosh\left( {{\frac{1}{w}}{({\rho})}}\right)}^{2}}}}} - {{{{{\phi_R}}^{2}}} {{{cosh\left( {{\frac{1}{w}}{({\rho})}}\right)}^{2}}}}}})}}}}{{{2}} {{{w}^{2}}} {{{sinh\left( {{\frac{1}{w}}{({\rho})}}\right)}^{2}}}} & 0 & 0 \\ \frac{{{{{{3}} {{{\phi_L}}} \cdot {{{{\phi_R}}^{2}}} {{{cosh\left( {{\frac{1}{w}}{({\rho})}}\right)}^{2}}}} - {{{3}} {{{\phi_L}}} \cdot {{{{\phi_R}}^{2}}} {{{sinh\left( {{\frac{1}{w}}{({\rho})}}\right)}^{2}}}}} - {{{6}} {{{\phi_L}}} \cdot {{{cosh\left( {{\frac{1}{w}}{({\rho})}}\right)}^{2}}}}} + {{{{{{\phi_L}}^{3}}} {{{cosh\left( {{\frac{1}{w}}{({\rho})}}\right)}^{2}}}} - {{{{{\phi_L}}^{3}}} {{{sinh\left( {{\frac{1}{w}}{({\rho})}}\right)}^{2}}}}} + {{{{6}} {{{\phi_L}}} \cdot {{{sinh\left( {{\frac{1}{w}}{({\rho})}}\right)}^{2}}}} - {{{3}} {{{\phi_R}}} \cdot {{{{\phi_L}}^{2}}} {{{cosh\left( {{\frac{1}{w}}{({\rho})}}\right)}^{2}}}}} + {{{{3}} {{{\phi_R}}} \cdot {{{{\phi_L}}^{2}}} {{{sinh\left( {{\frac{1}{w}}{({\rho})}}\right)}^{2}}}} - {{{{{\phi_R}}^{3}}} {{{cosh\left( {{\frac{1}{w}}{({\rho})}}\right)}^{2}}}}} + {{{{6}} {{{\phi_R}}} \cdot {{{cosh\left( {{\frac{1}{w}}{({\rho})}}\right)}^{2}}}} - {{{6}} {{{\phi_R}}} \cdot {{{sinh\left( {{\frac{1}{w}}{({\rho})}}\right)}^{2}}}}} + {{{{{\phi_R}}^{3}}} {{{sinh\left( {{\frac{1}{w}}{({\rho})}}\right)}^{2}}}}}{{{6}} {{{w}^{2}}} {{{sinh\left( {{\frac{1}{w}}{({\rho})}}\right)}^{2}}}} & 0 & 0\end{matrix}\right]}$
${{\frac{\partial}{\partial \theta}}\left({{\left[\begin{matrix} {\frac{1}{2}}{({-{({{{{{\phi_L}}^{2}} - {{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}} \cdot {{{cos\left( \theta\right)}^{2}}}} - {{{{{\phi_L}}^{2}}} {{{cos\left( \theta\right)}^{2}}}}} + {{{{\phi_R}}^{2}} - {{{{{\phi_R}}^{2}}} {{{cos\left( \theta\right)}^{2}}}}}})}})} & \frac{{{w}} {{({{{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_L}}^{2}}} - {{{\phi_R}}^{2}}})}} {{sin\left( \theta\right)}} {{cos\left( \theta\right)}} {{sinh\left( {{\frac{1}{w}}{({\rho})}}\right)}}}{{{2}} {{cosh\left( {{\frac{1}{w}}{({\rho})}}\right)}}} & \frac{{{w}} {{sinh\left( {{\frac{1}{w}}{({\rho})}}\right)}} {{({{{{{3}} {{{\phi_L}}} \cdot {{{{\phi_R}}^{2}}} {{{cos\left( \theta\right)}^{4}}}} - {{{9}} {{{\phi_L}}} \cdot {{{{\phi_R}}^{2}}} {{{cos\left( \theta\right)}^{2}}}}} + {{{{3}} {{{\phi_L}}} \cdot {{{{\phi_R}}^{2}}} {{{cos\left( \theta\right)}^{2}}} {{{sin\left( \theta\right)}^{2}}}} - {{{3}} {{{\phi_L}}} \cdot {{{{\phi_R}}^{2}}} {{{sin\left( \theta\right)}^{2}}}}} + {{{6}} {{{\phi_L}}} \cdot {{{{\phi_R}}^{2}}}} + {{{{{6}} {{{\phi_L}}} \cdot {{{cos\left( \theta\right)}^{2}}}} - {{{6}} {{{\phi_L}}}}} - {{{3}} {{{\phi_R}}} \cdot {{{{\phi_L}}^{2}}} {{{cos\left( \theta\right)}^{4}}}}} + {{{{9}} {{{\phi_R}}} \cdot {{{{\phi_L}}^{2}}} {{{cos\left( \theta\right)}^{2}}}} - {{{3}} {{{\phi_R}}} \cdot {{{{\phi_L}}^{2}}} {{{cos\left( \theta\right)}^{2}}} {{{sin\left( \theta\right)}^{2}}}}} + {{{{{3}} {{{\phi_R}}} \cdot {{{{\phi_L}}^{2}}} {{{sin\left( \theta\right)}^{2}}}} - {{{6}} {{{\phi_R}}} \cdot {{{{\phi_L}}^{2}}}}} - {{{6}} {{{\phi_R}}} \cdot {{{cos\left( \theta\right)}^{2}}}}} + {{{6}} {{{\phi_R}}}} + {{{{{\phi_L}}^{3}}} {{{cos\left( \theta\right)}^{2}}} {{{sin\left( \theta\right)}^{2}}}} + {{{{{{{\phi_L}}^{3}}} {{{cos\left( \theta\right)}^{4}}}} - {{{3}} {{{{\phi_L}}^{3}}} {{{cos\left( \theta\right)}^{2}}}}} - {{{{{\phi_L}}^{3}}} {{{sin\left( \theta\right)}^{2}}}}} + {{{2}} {{{{\phi_L}}^{3}}}} + {{{{{3}} {{{{\phi_R}}^{3}}} {{{cos\left( \theta\right)}^{2}}}} - {{{{{\phi_R}}^{3}}} {{{cos\left( \theta\right)}^{4}}}}} - {{{{{\phi_R}}^{3}}} {{{sin\left( \theta\right)}^{2}}} {{{cos\left( \theta\right)}^{2}}}}} + {{{{{{\phi_R}}^{3}}} {{{sin\left( \theta\right)}^{2}}}} - {{{2}} {{{{\phi_R}}^{3}}}}}})}}}{{{6}} {{cosh\left( {{\frac{1}{w}}{({\rho})}}\right)}}} \\ \frac{-{{{{({{{\phi_L}} - {{\phi_R}}})}^{2}}} {{sin\left( \theta\right)}} {{cos\left( \theta\right)}} {{cosh\left( {{\frac{1}{w}}{({\rho})}}\right)}}}}{{{2}} {{w}} {{sinh\left( {{\frac{1}{w}}{({\rho})}}\right)}}} & {\frac{1}{2}}{({{{{cos\left( \theta\right)}^{2}}} {{({{{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_L}}^{2}}} - {{{\phi_R}}^{2}}})}}})} & {\frac{1}{6}}{({{{sin\left( \theta\right)}} {{cos\left( \theta\right)}} {{({{{{{{3}} {{{\phi_L}}} \cdot {{{{\phi_R}}^{2}}}} - {{{6}} {{{\phi_L}}}}} - {{{3}} {{{\phi_R}}} \cdot {{{{\phi_L}}^{2}}}}} + {{{{6}} {{{\phi_R}}}} - {{{\phi_R}}^{3}}} + {{{\phi_L}}^{3}}})}}})} \\ \frac{-{{{cosh\left( {{\frac{1}{w}}{({\rho})}}\right)}} {{({{{{3}} {{{\phi_L}}} \cdot {{{{\phi_R}}^{2}}}} + {{{{{\phi_L}}^{3}} - {{{6}} {{{\phi_L}}}}} - {{{3}} {{{\phi_R}}} \cdot {{{{\phi_L}}^{2}}}}} + {{{{6}} {{{\phi_R}}}} - {{{\phi_R}}^{3}}}})}}}}{{{6}} {{w}} {{sinh\left( {{\frac{1}{w}}{({\rho})}}\right)}}} & \frac{-{{{cos\left( \theta\right)}} {{({{{{3}} {{{\phi_L}}} \cdot {{{{\phi_R}}^{2}}}} + {{{{{\phi_L}}^{3}} - {{{6}} {{{\phi_L}}}}} - {{{3}} {{{\phi_R}}} \cdot {{{{\phi_L}}^{2}}}}} + {{{{6}} {{{\phi_R}}}} - {{{\phi_R}}^{3}}}})}}}}{{{6}} {{sin\left( \theta\right)}}} & {\frac{1}{2}}{({-{({{{{{\phi_L}}^{2}} - {{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}}} + {{{\phi_R}}^{2}}})}})}\end{matrix}\right]} + {{\mathcal{O}(A^4)}}}\right)} = {\left[\begin{matrix} {{sin\left( \theta\right)}} {{cos\left( \theta\right)}} {{({{{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_L}}^{2}}} - {{{\phi_R}}^{2}}})}} & \frac{{{w}} {{sinh\left( {{\frac{1}{w}}{({\rho})}}\right)}} {{({{{{{{4}} {{{\phi_L}}} \cdot {{{\phi_R}}} \cdot {{{cos\left( \theta\right)}^{2}}}} - {{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}}} - {{{2}} {{{{\phi_L}}^{2}}} {{{cos\left( \theta\right)}^{2}}}}} + {{{{\phi_L}}^{2}} - {{{2}} {{{{\phi_R}}^{2}}} {{{cos\left( \theta\right)}^{2}}}}} + {{{\phi_R}}^{2}}})}}}{{{2}} {{cosh\left( {{\frac{1}{w}}{({\rho})}}\right)}}} & \frac{{{w}} {{({{{{{{3}} {{{\phi_L}}} \cdot {{{{\phi_R}}^{2}}}} - {{{6}} {{{\phi_L}}}}} - {{{3}} {{{\phi_R}}} \cdot {{{{\phi_L}}^{2}}}}} + {{{6}} {{{\phi_R}}}} + {{{{\phi_L}}^{3}} - {{{\phi_R}}^{3}}}})}} {{sin\left( \theta\right)}} {{sinh\left( {{\frac{1}{w}}{({\rho})}}\right)}} {{cos\left( \theta\right)}}}{{{3}} {{cosh\left( {{\frac{1}{w}}{({\rho})}}\right)}}} \\ \frac{{{cosh\left( {{\frac{1}{w}}{({\rho})}}\right)}} {{({{{{{{4}} {{{\phi_L}}} \cdot {{{\phi_R}}} \cdot {{{cos\left( \theta\right)}^{2}}}} - {{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}}} - {{{2}} {{{{\phi_L}}^{2}}} {{{cos\left( \theta\right)}^{2}}}}} + {{{{\phi_L}}^{2}} - {{{2}} {{{{\phi_R}}^{2}}} {{{cos\left( \theta\right)}^{2}}}}} + {{{\phi_R}}^{2}}})}}}{{{2}} {{w}} {{sinh\left( {{\frac{1}{w}}{({\rho})}}\right)}}} & -{{{sin\left( \theta\right)}} {{cos\left( \theta\right)}} {{({{{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_L}}^{2}}} - {{{\phi_R}}^{2}}})}}} & {\frac{1}{6}}{({-{({{{{{\phi_L}}^{3}} - {{{6}} {{{\phi_L}}}}} + {{{{{3}} {{{\phi_L}}} \cdot {{{{\phi_R}}^{2}}}} - {{{6}} {{{\phi_L}}} \cdot {{{{\phi_R}}^{2}}} {{{cos\left( \theta\right)}^{2}}}}} - {{{2}} {{{{\phi_L}}^{3}}} {{{cos\left( \theta\right)}^{2}}}}} + {{{12}} {{{\phi_L}}} \cdot {{{cos\left( \theta\right)}^{2}}}} + {{{{{6}} {{{\phi_R}}}} - {{{\phi_R}}^{3}}} - {{{3}} {{{\phi_R}}} \cdot {{{{\phi_L}}^{2}}}}} + {{{{6}} {{{\phi_R}}} \cdot {{{{\phi_L}}^{2}}} {{{cos\left( \theta\right)}^{2}}}} - {{{12}} {{{\phi_R}}} \cdot {{{cos\left( \theta\right)}^{2}}}}} + {{{2}} {{{{\phi_R}}^{3}}} {{{cos\left( \theta\right)}^{2}}}}})}})} \\ 0 & \frac{{{{{3}} {{{\phi_L}}} \cdot {{{{\phi_R}}^{2}}}} - {{{6}} {{{\phi_L}}}}} + {{{{{\phi_L}}^{3}} - {{{3}} {{{\phi_R}}} \cdot {{{{\phi_L}}^{2}}}}} - {{{\phi_R}}^{3}}} + {{{6}} {{{\phi_R}}}}}{{{6}} {{({{1} - {{cos\left( \theta\right)}^{2}}})}}} & 0\end{matrix}\right]}$
${{\frac{\partial}{\partial \phi}}\left({{\left[\begin{matrix} {\frac{1}{2}}{({-{({{{{{\phi_L}}^{2}} - {{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}} \cdot {{{cos\left( \theta\right)}^{2}}}} - {{{{{\phi_L}}^{2}}} {{{cos\left( \theta\right)}^{2}}}}} + {{{{\phi_R}}^{2}} - {{{{{\phi_R}}^{2}}} {{{cos\left( \theta\right)}^{2}}}}}})}})} & \frac{{{w}} {{({{{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_L}}^{2}}} - {{{\phi_R}}^{2}}})}} {{sin\left( \theta\right)}} {{cos\left( \theta\right)}} {{sinh\left( {{\frac{1}{w}}{({\rho})}}\right)}}}{{{2}} {{cosh\left( {{\frac{1}{w}}{({\rho})}}\right)}}} & \frac{{{w}} {{sinh\left( {{\frac{1}{w}}{({\rho})}}\right)}} {{({{{{{3}} {{{\phi_L}}} \cdot {{{{\phi_R}}^{2}}} {{{cos\left( \theta\right)}^{4}}}} - {{{9}} {{{\phi_L}}} \cdot {{{{\phi_R}}^{2}}} {{{cos\left( \theta\right)}^{2}}}}} + {{{{3}} {{{\phi_L}}} \cdot {{{{\phi_R}}^{2}}} {{{cos\left( \theta\right)}^{2}}} {{{sin\left( \theta\right)}^{2}}}} - {{{3}} {{{\phi_L}}} \cdot {{{{\phi_R}}^{2}}} {{{sin\left( \theta\right)}^{2}}}}} + {{{6}} {{{\phi_L}}} \cdot {{{{\phi_R}}^{2}}}} + {{{{{6}} {{{\phi_L}}} \cdot {{{cos\left( \theta\right)}^{2}}}} - {{{6}} {{{\phi_L}}}}} - {{{3}} {{{\phi_R}}} \cdot {{{{\phi_L}}^{2}}} {{{cos\left( \theta\right)}^{4}}}}} + {{{{9}} {{{\phi_R}}} \cdot {{{{\phi_L}}^{2}}} {{{cos\left( \theta\right)}^{2}}}} - {{{3}} {{{\phi_R}}} \cdot {{{{\phi_L}}^{2}}} {{{cos\left( \theta\right)}^{2}}} {{{sin\left( \theta\right)}^{2}}}}} + {{{{{3}} {{{\phi_R}}} \cdot {{{{\phi_L}}^{2}}} {{{sin\left( \theta\right)}^{2}}}} - {{{6}} {{{\phi_R}}} \cdot {{{{\phi_L}}^{2}}}}} - {{{6}} {{{\phi_R}}} \cdot {{{cos\left( \theta\right)}^{2}}}}} + {{{6}} {{{\phi_R}}}} + {{{{{\phi_L}}^{3}}} {{{cos\left( \theta\right)}^{2}}} {{{sin\left( \theta\right)}^{2}}}} + {{{{{{{\phi_L}}^{3}}} {{{cos\left( \theta\right)}^{4}}}} - {{{3}} {{{{\phi_L}}^{3}}} {{{cos\left( \theta\right)}^{2}}}}} - {{{{{\phi_L}}^{3}}} {{{sin\left( \theta\right)}^{2}}}}} + {{{2}} {{{{\phi_L}}^{3}}}} + {{{{{3}} {{{{\phi_R}}^{3}}} {{{cos\left( \theta\right)}^{2}}}} - {{{{{\phi_R}}^{3}}} {{{cos\left( \theta\right)}^{4}}}}} - {{{{{\phi_R}}^{3}}} {{{sin\left( \theta\right)}^{2}}} {{{cos\left( \theta\right)}^{2}}}}} + {{{{{{\phi_R}}^{3}}} {{{sin\left( \theta\right)}^{2}}}} - {{{2}} {{{{\phi_R}}^{3}}}}}})}}}{{{6}} {{cosh\left( {{\frac{1}{w}}{({\rho})}}\right)}}} \\ \frac{-{{{{({{{\phi_L}} - {{\phi_R}}})}^{2}}} {{sin\left( \theta\right)}} {{cos\left( \theta\right)}} {{cosh\left( {{\frac{1}{w}}{({\rho})}}\right)}}}}{{{2}} {{w}} {{sinh\left( {{\frac{1}{w}}{({\rho})}}\right)}}} & {\frac{1}{2}}{({{{{cos\left( \theta\right)}^{2}}} {{({{{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_L}}^{2}}} - {{{\phi_R}}^{2}}})}}})} & {\frac{1}{6}}{({{{sin\left( \theta\right)}} {{cos\left( \theta\right)}} {{({{{{{{3}} {{{\phi_L}}} \cdot {{{{\phi_R}}^{2}}}} - {{{6}} {{{\phi_L}}}}} - {{{3}} {{{\phi_R}}} \cdot {{{{\phi_L}}^{2}}}}} + {{{{6}} {{{\phi_R}}}} - {{{\phi_R}}^{3}}} + {{{\phi_L}}^{3}}})}}})} \\ \frac{-{{{cosh\left( {{\frac{1}{w}}{({\rho})}}\right)}} {{({{{{3}} {{{\phi_L}}} \cdot {{{{\phi_R}}^{2}}}} + {{{{{\phi_L}}^{3}} - {{{6}} {{{\phi_L}}}}} - {{{3}} {{{\phi_R}}} \cdot {{{{\phi_L}}^{2}}}}} + {{{{6}} {{{\phi_R}}}} - {{{\phi_R}}^{3}}}})}}}}{{{6}} {{w}} {{sinh\left( {{\frac{1}{w}}{({\rho})}}\right)}}} & \frac{-{{{cos\left( \theta\right)}} {{({{{{3}} {{{\phi_L}}} \cdot {{{{\phi_R}}^{2}}}} + {{{{{\phi_L}}^{3}} - {{{6}} {{{\phi_L}}}}} - {{{3}} {{{\phi_R}}} \cdot {{{{\phi_L}}^{2}}}}} + {{{{6}} {{{\phi_R}}}} - {{{\phi_R}}^{3}}}})}}}}{{{6}} {{sin\left( \theta\right)}}} & {\frac{1}{2}}{({-{({{{{{\phi_L}}^{2}} - {{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}}} + {{{\phi_R}}^{2}}})}})}\end{matrix}\right]} + {{\mathcal{O}(A^4)}}}\right)} = {\left[\begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{matrix}\right]}$
volume element: ${{{({\frac{{{A}} {{sinh\left( {{\frac{1}{w}}{({\rho})}}\right)}}}{sinh\left( {\frac{1}{w}}\right)}})}^{2}}} {{sin\left( \theta\right)}}$
volume integral: ${{({\int\limits_{{{\theta_L}}}^{{{\theta_R}}}d \theta\left({\int\limits_{{{\rho_L}}}^{{{\rho_R}}}d \rho\left({\frac{{{{A}^{2}}} {{{sinh\left( {{\frac{1}{w}}{({\rho})}}\right)}^{2}}} {{sin\left( \theta\right)}}}{{sinh\left( {\frac{1}{w}}\right)}^{2}}}\right)}\right)})}} {{\Delta \phi}}$
finite volume (0,0)-form:
${{u(x_C, t_R)}} = {{{u(x_C, t_L)}} + {{{\Delta t}} \cdot {{({{{{\frac{1}{{\mathcal{V}(x_C)}}}} {{({{{-{({\int\limits_{{{\phi_L}}}^{{{\phi_R}}}d \phi\left({\int\limits_{{{\theta_L}}}^{{{\theta_R}}}d \theta\left({{{{{J(\rho_R)}}} \cdot {{{{e_{\rho}}^{\bar{\rho}}(\rho_R)}}} \cdot {{{F^{\rho}(\rho_R)}}}} - {{{{J(\rho_L)}}} \cdot {{{{e_{\rho}}^{\bar{\rho}}(\rho_L)}}} \cdot {{{F^{\rho}(\rho_L)}}}}}\right)}\right)})}} - {({\int\limits_{{{\phi_L}}}^{{{\phi_R}}}d \phi\left({\int\limits_{{{\rho_L}}}^{{{\rho_R}}}d \rho\left({{{{{J(\theta_R)}}} \cdot {{{{e_{\theta}}^{\bar{\theta}}(\theta_R)}}} \cdot {{{F^{\theta}(\theta_R)}}}} - {{{{J(\theta_L)}}} \cdot {{{{e_{\theta}}^{\bar{\theta}}(\theta_L)}}} \cdot {{{F^{\theta}(\theta_L)}}}}}\right)}\right)})}} - {({\int\limits_{{{\theta_L}}}^{{{\theta_R}}}d \theta\left({\int\limits_{{{\rho_L}}}^{{{\rho_R}}}d \rho\left({{{{{J(\phi_R)}}} \cdot {{{{e_{\phi}}^{\bar{\phi}}(\phi_R)}}} \cdot {{{F^{\phi}(\phi_R)}}}} - {{{{J(\phi_L)}}} \cdot {{{{e_{\phi}}^{\bar{\phi}}(\phi_L)}}} \cdot {{{F^{\phi}(\phi_L)}}}}}\right)}\right)})}})}}} + {{S(x_C)}}})}}}}$
${{u(x_C, t_R)}} = {{{u(x_C, t_L)}} + {{{\Delta t}} \cdot {{({{{{\frac{1}{{{({\int\limits_{{{\theta_L}}}^{{{\theta_R}}}d \theta\left({\int\limits_{{{\rho_L}}}^{{{\rho_R}}}d \rho\left({\frac{{{{A}^{2}}} {{{sinh\left( {{\frac{1}{w}}{({\rho})}}\right)}^{2}}} {{sin\left( \theta\right)}}}{{sinh\left( {\frac{1}{w}}\right)}^{2}}}\right)}\right)})}} {{\Delta \phi}}}}} {{({{{-{({\int\limits_{{{\phi_L}}}^{{{\phi_R}}}d \phi\left({\int\limits_{{{\theta_L}}}^{{{\theta_R}}}d \theta\left({{{{{({\frac{{{A}} {{sinh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)}}}{sinh\left( {\frac{1}{w}}\right)}})}^{2}}} {{sin\left( \theta\right)}} {{{F^{\rho}(\rho_R)}}}} - {{{{({\frac{{{A}} {{sinh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}}}{sinh\left( {\frac{1}{w}}\right)}})}^{2}}} {{sin\left( \theta\right)}} {{{F^{\rho}(\rho_L)}}}}}\right)}\right)})}} - {({\int\limits_{{{\phi_L}}}^{{{\phi_R}}}d \phi\left({\int\limits_{{{\rho_L}}}^{{{\rho_R}}}d \rho\left({{{{{({\frac{{{A}} {{sinh\left( {{\frac{1}{w}}{({\rho})}}\right)}}}{sinh\left( {\frac{1}{w}}\right)}})}^{2}}} {{sin\left( {\theta_R}\right)}} {{{F^{\theta}(\theta_R)}}}} - {{{{({\frac{{{A}} {{sinh\left( {{\frac{1}{w}}{({\rho})}}\right)}}}{sinh\left( {\frac{1}{w}}\right)}})}^{2}}} {{sin\left( {\theta_L}\right)}} {{{F^{\theta}(\theta_L)}}}}}\right)}\right)})}} - {({\int\limits_{{{\theta_L}}}^{{{\theta_R}}}d \theta\left({\int\limits_{{{\rho_L}}}^{{{\rho_R}}}d \rho\left({{{{{({\frac{{{A}} {{sinh\left( {{\frac{1}{w}}{({\rho})}}\right)}}}{sinh\left( {\frac{1}{w}}\right)}})}^{2}}} {{sin\left( \theta\right)}} {{{F^{\phi}(\phi_R)}}}} - {{{{({\frac{{{A}} {{sinh\left( {{\frac{1}{w}}{({\rho})}}\right)}}}{sinh\left( {\frac{1}{w}}\right)}})}^{2}}} {{sin\left( \theta\right)}} {{{F^{\phi}(\phi_L)}}}}}\right)}\right)})}})}}} + {{S(x_C)}}})}}}}$
${{u(x_C, t_R)}} = {{{u(x_C, t_L)}} + {{{\Delta t}} \cdot {{({{{{\frac{1}{{{({\int\limits_{{{\theta_L}}}^{{{\theta_R}}}d \theta\left({\int\limits_{{{\rho_L}}}^{{{\rho_R}}}d \rho\left({\frac{{{{A}^{2}}} {{{sinh\left( {{\frac{1}{w}}{({\rho})}}\right)}^{2}}} {{sin\left( \theta\right)}}}{{sinh\left( {\frac{1}{w}}\right)}^{2}}}\right)}\right)})}} {{\Delta \phi}}}}} {{({{{-{{{\frac{-{{{{A}^{2}}} {{({{{{{{{F^{\rho}(\rho_L)}}} \cdot {{{sinh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}^{2}}} {{cos\left( {\theta_L}\right)}}} - {{{{F^{\rho}(\rho_L)}}} \cdot {{{sinh\left( {{\frac{1}{w}}{({{\rho_L}})}}\right)}^{2}}} {{cos\left( {\theta_R}\right)}}}} - {{{{F^{\rho}(\rho_R)}}} \cdot {{{sinh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)}^{2}}} {{cos\left( {\theta_L}\right)}}}} + {{{{F^{\rho}(\rho_R)}}} \cdot {{{sinh\left( {{\frac{1}{w}}{({{\rho_R}})}}\right)}^{2}}} {{cos\left( {\theta_R}\right)}}}})}}}}{{sinh\left( {\frac{1}{w}}\right)}^{2}}}} {{\Delta \phi}}}} - {{{({\int\limits_{{{\rho_L}}}^{{{\rho_R}}}d \rho\left({\frac{{{{A}^{2}}} {{{sinh\left( {{\frac{1}{w}}{({\rho})}}\right)}^{2}}} {{({{{{{F^{\theta}(\theta_R)}}} \cdot {{sin\left( {\theta_R}\right)}}} - {{{{F^{\theta}(\theta_L)}}} \cdot {{sin\left( {\theta_L}\right)}}}})}}}{{sinh\left( {\frac{1}{w}}\right)}^{2}}}\right)})}} {{\Delta \phi}}}} - {({\int\limits_{{{\theta_L}}}^{{{\theta_R}}}d \theta\left({\int\limits_{{{\rho_L}}}^{{{\rho_R}}}d \rho\left({\frac{-{{{{A}^{2}}} {{{sinh\left( {{\frac{1}{w}}{({\rho})}}\right)}^{2}}} {{sin\left( \theta\right)}} {{({{{F^{\phi}(\phi_L)}} - {{F^{\phi}(\phi_R)}}})}}}}{{sinh\left( {\frac{1}{w}}\right)}^{2}}}\right)}\right)})}})}}} + {{S(x_C)}}})}}}}$
${{u(x_C, t_R)}} = {{{u(x_C, t_L)}} + {{{{S(x_C)}}} \cdot {{\Delta t}}} + {{{-1}} {{\Delta t}} \cdot {{({\int\limits_{{{\theta_L}}}^{{{\theta_R}}}d \theta\left({\int\limits_{{{\rho_L}}}^{{{\rho_R}}}d \rho\left({{{{-1}} {{{A}^{2}}} {{{sinh\left( {{{\rho}} \cdot {{\frac{1}{w}}}}\right)}^{2}}} {{sin\left( \theta\right)}} {{{F^{\phi}(\phi_L)}}} \cdot {{\frac{1}{{sinh\left( {\frac{1}{w}}\right)}^{2}}}}} - {{{-1}} {{{A}^{2}}} {{{sinh\left( {{{\rho}} \cdot {{\frac{1}{w}}}}\right)}^{2}}} {{sin\left( \theta\right)}} {{{F^{\phi}(\phi_R)}}} \cdot {{\frac{1}{{sinh\left( {\frac{1}{w}}\right)}^{2}}}}}}\right)}\right)})}} {{\frac{1}{\Delta \phi}}} {{\frac{1}{\int\limits_{{{\theta_L}}}^{{{\theta_R}}}d \theta\left({\int\limits_{{{\rho_L}}}^{{{\rho_R}}}d \rho\left({{{{A}^{2}}} {{{sinh\left( {{{\rho}} \cdot {{\frac{1}{w}}}}\right)}^{2}}} {{sin\left( \theta\right)}} {{\frac{1}{{sinh\left( {\frac{1}{w}}\right)}^{2}}}}}\right)}\right)}}}} + {{{-1}} {{\Delta t}} \cdot {{({\int\limits_{{{\rho_L}}}^{{{\rho_R}}}d \rho\left({{{{{A}^{2}}} {{{sinh\left( {{{\rho}} \cdot {{\frac{1}{w}}}}\right)}^{2}}} {{{F^{\theta}(\theta_R)}}} \cdot {{sin\left( {\theta_R}\right)}} {{\frac{1}{{sinh\left( {\frac{1}{w}}\right)}^{2}}}}} - {{{{A}^{2}}} {{{sinh\left( {{{\rho}} \cdot {{\frac{1}{w}}}}\right)}^{2}}} {{{F^{\theta}(\theta_L)}}} \cdot {{sin\left( {\theta_L}\right)}} {{\frac{1}{{sinh\left( {\frac{1}{w}}\right)}^{2}}}}}}\right)})}} {{\frac{1}{\int\limits_{{{\theta_L}}}^{{{\theta_R}}}d \theta\left({\int\limits_{{{\rho_L}}}^{{{\rho_R}}}d \rho\left({{{{A}^{2}}} {{{sinh\left( {{{\rho}} \cdot {{\frac{1}{w}}}}\right)}^{2}}} {{sin\left( \theta\right)}} {{\frac{1}{{sinh\left( {\frac{1}{w}}\right)}^{2}}}}}\right)}\right)}}}} + {{{{F^{\rho}(\rho_L)}}} \cdot {{\Delta t}} \cdot {{{A}^{2}}} {{{sinh\left( {{{{\rho_L}}} \cdot {{\frac{1}{w}}}}\right)}^{2}}} {{cos\left( {\theta_L}\right)}} {{\frac{1}{{sinh\left( {\frac{1}{w}}\right)}^{2}}}} {{\frac{1}{\int\limits_{{{\theta_L}}}^{{{\theta_R}}}d \theta\left({\int\limits_{{{\rho_L}}}^{{{\rho_R}}}d \rho\left({{{{A}^{2}}} {{{sinh\left( {{{\rho}} \cdot {{\frac{1}{w}}}}\right)}^{2}}} {{sin\left( \theta\right)}} {{\frac{1}{{sinh\left( {\frac{1}{w}}\right)}^{2}}}}}\right)}\right)}}}} + {{{-1}} {{{F^{\rho}(\rho_L)}}} \cdot {{\Delta t}} \cdot {{{A}^{2}}} {{{sinh\left( {{{{\rho_L}}} \cdot {{\frac{1}{w}}}}\right)}^{2}}} {{cos\left( {\theta_R}\right)}} {{\frac{1}{{sinh\left( {\frac{1}{w}}\right)}^{2}}}} {{\frac{1}{\int\limits_{{{\theta_L}}}^{{{\theta_R}}}d \theta\left({\int\limits_{{{\rho_L}}}^{{{\rho_R}}}d \rho\left({{{{A}^{2}}} {{{sinh\left( {{{\rho}} \cdot {{\frac{1}{w}}}}\right)}^{2}}} {{sin\left( \theta\right)}} {{\frac{1}{{sinh\left( {\frac{1}{w}}\right)}^{2}}}}}\right)}\right)}}}} + {{{-1}} {{{F^{\rho}(\rho_R)}}} \cdot {{\Delta t}} \cdot {{{A}^{2}}} {{{sinh\left( {{{{\rho_R}}} \cdot {{\frac{1}{w}}}}\right)}^{2}}} {{cos\left( {\theta_L}\right)}} {{\frac{1}{{sinh\left( {\frac{1}{w}}\right)}^{2}}}} {{\frac{1}{\int\limits_{{{\theta_L}}}^{{{\theta_R}}}d \theta\left({\int\limits_{{{\rho_L}}}^{{{\rho_R}}}d \rho\left({{{{A}^{2}}} {{{sinh\left( {{{\rho}} \cdot {{\frac{1}{w}}}}\right)}^{2}}} {{sin\left( \theta\right)}} {{\frac{1}{{sinh\left( {\frac{1}{w}}\right)}^{2}}}}}\right)}\right)}}}} + {{{{F^{\rho}(\rho_R)}}} \cdot {{\Delta t}} \cdot {{{A}^{2}}} {{{sinh\left( {{{{\rho_R}}} \cdot {{\frac{1}{w}}}}\right)}^{2}}} {{cos\left( {\theta_R}\right)}} {{\frac{1}{{sinh\left( {\frac{1}{w}}\right)}^{2}}}} {{\frac{1}{\int\limits_{{{\theta_L}}}^{{{\theta_R}}}d \theta\left({\int\limits_{{{\rho_L}}}^{{{\rho_R}}}d \rho\left({{{{A}^{2}}} {{{sinh\left( {{{\rho}} \cdot {{\frac{1}{w}}}}\right)}^{2}}} {{sin\left( \theta\right)}} {{\frac{1}{{sinh\left( {\frac{1}{w}}\right)}^{2}}}}}\right)}\right)}}}}}$