spherical and time, coordinate
chart coordinates: $x^\tilde{\mu} = \{t, r, \theta, \phi\}$
chart coordinate basis: $e_\tilde{\mu} = \{e_{\tilde{t}}, e_{\tilde{r}}, e_{\tilde{\theta}}, e_{\tilde{\phi}}\}$
embedding coordinates: $u^I = \{t, x, y, z\}$
embedding basis $e_I = \{e_{t}, e_{x}, e_{y}, e_{z}\}$
transform from basis to coordinate:
${{{ \tilde{e}}_t}^t} = {1}$;
${{{ \tilde{e}}_r}^r} = {1}$;
${{{ \tilde{e}}_{\theta}}^{\theta}} = {1}$;
${{{ \tilde{e}}_{\phi}}^{\phi}} = {1}$
transform from coorinate to basis:
${{{ \tilde{e}}^t}_t} = {1}$;
${{{ \tilde{e}}^r}_r} = {1}$;
${{{ \tilde{e}}^{\theta}}_{\theta}} = {1}$;
${{{ \tilde{e}}^{\phi}}_{\phi}} = {1}$
tensor index associated with coordinate $t$ is index $t$ with operator $e_{t}(\zeta) = $$\frac{\partial \zeta}{\partial t}$
tensor index associated with coordinate $r$ is index $r$ with operator $e_{r}(\zeta) = $$\frac{\partial \zeta}{\partial r}$
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:
${{{ \eta}_t}_t} = {-1}$;
${{{ \eta}_x}_x} = {1}$;
${{{ \eta}_y}_y} = {1}$;
${{{ \eta}_z}_z} = {1}$
chart in embedded coordinates:
${{ u}^t} = {t}$;
${{ u}^x} = {{{r}} {{sin\left( \theta\right)}} {{cos\left( \phi\right)}}}$;
${{ u}^y} = {{{r}} {{sin\left( \theta\right)}} {{sin\left( \phi\right)}}}$;
${{ u}^z} = {{{r}} {{cos\left( \theta\right)}}}$
basis operators applied to chart:
${{{ e}_u}^I} = {{{ u}^I}_{,u}}$
${{{ e}_t}^t} = {1}$;
${{{ e}_r}^x} = {{{sin\left( \theta\right)}} {{cos\left( \phi\right)}}}$;
${{{ e}_r}^y} = {{{sin\left( \theta\right)}} {{sin\left( \phi\right)}}}$;
${{{ e}_r}^z} = {cos\left( \theta\right)}$;
${{{ e}_{\theta}}^x} = {{{r}} {{cos\left( \theta\right)}} {{cos\left( \phi\right)}}}$;
${{{ e}_{\theta}}^y} = {{{r}} {{cos\left( \theta\right)}} {{sin\left( \phi\right)}}}$;
${{{ e}_{\theta}}^z} = {-{{{r}} {{sin\left( \theta\right)}}}}$;
${{{ e}_{\phi}}^x} = {-{{{r}} {{sin\left( \theta\right)}} {{sin\left( \phi\right)}}}}$;
${{{ e}_{\phi}}^y} = {{{r}} {{sin\left( \theta\right)}} {{cos\left( \phi\right)}}}$
${{{ e}^t}_t} = {1}$;
${{{ e}^r}_x} = {{{cos\left( \phi\right)}} {{sin\left( \theta\right)}}}$;
${{{ e}^r}_y} = {{{sin\left( \theta\right)}} {{sin\left( \phi\right)}}}$;
${{{ e}^r}_z} = {cos\left( \theta\right)}$;
${{{ e}^{\theta}}_x} = {{\frac{1}{r}}{({{{cos\left( \phi\right)}} {{cos\left( \theta\right)}}})}}$;
${{{ e}^{\theta}}_y} = {{\frac{1}{r}}{({{{cos\left( \theta\right)}} {{sin\left( \phi\right)}}})}}$;
${{{ e}^{\theta}}_z} = {\frac{sin\left( \theta\right)}{-{r}}}$;
${{{ e}^{\phi}}_x} = {\frac{-{sin\left( \phi\right)}}{{{r}} {{sin\left( \theta\right)}}}}$;
${{{ e}^{\phi}}_y} = {\frac{cos\left( \phi\right)}{{{r}} {{sin\left( \theta\right)}}}}$
${{{{{ e}_u}^I}} {{{{ e}^v}_I}}} = {\overset{u\downarrow v\rightarrow}{\left[\begin{matrix} 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 1\end{matrix}\right]}}$
${{{{{ e}_u}^I}} {{{{ e}^u}_J}}} = {\overset{I\downarrow J\rightarrow}{\left[\begin{matrix} 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 1\end{matrix}\right]}}$
basis determinant: ${det(e)} = {{{{r}^{2}}} {{sin\left( \theta\right)}}}$
${{{{ c}_a}_b}^c} = {0}$
${{{ g}_u}_v} = {{{{{ e}_u}^I}} {{{{ e}_v}^J}} {{{{ \eta}_I}_J}}}$
${{{ g}_t}_t} = {-{1}}$;
${{{ g}_r}_r} = {1}$;
${{{ g}_{\theta}}_{\theta}} = {{r}^{2}}$;
${{{ g}_{\phi}}_{\phi}} = {{{{r}^{2}}} {{({{1} - {{cos\left( \theta\right)}^{2}}})}}}$
${{{ g}_u}_v} = {{{{{ e}_u}^I}} {{{{ e}_v}^J}} {{{{ \eta}_I}_J}}}$
metric determinant: ${det(g)} = {-{{{{r}^{4}}} {{({{1} - {{cos\left( \theta\right)}^{2}}})}}}}$
${{{{ \Gamma}_a}_b}_c} = {{{{\frac{1}{2}}{({1})}}} {{({{{{{{{{ g}_a}_b}_{,c}} + {{{{ g}_a}_c}_{,b}}} - {{{{ g}_b}_c}_{,a}}} + {{{{ c}_a}_b}_c} + {{{{ c}_a}_c}_b}} - {{{{ c}_c}_b}_a}})}}}$
commutation coefficients:
${{{{ c}_a}_b}^c} = {0}$
metric:
${{{ g}_t}_t} = {-{1}}$;
${{{ g}_r}_r} = {1}$;
${{{ g}_{\theta}}_{\theta}} = {{r}^{2}}$;
${{{ g}_{\phi}}_{\phi}} = {{{{r}^{2}}} {{({{1} - {{cos\left( \theta\right)}^{2}}})}}}$
metric inverse:
${{{ g}^t}^t} = {-{1}}$;
${{{ g}^r}^r} = {1}$;
${{{ g}^{\theta}}^{\theta}} = {\frac{1}{{r}^{2}}}$;
${{{ g}^{\phi}}^{\phi}} = {\frac{1}{{{{r}^{2}}} {{({{1} - {{cos\left( \theta\right)}^{2}}})}}}}$
metric derivative:
${{{{ {\partial g}}_{\theta}}_{\theta}}_r} = {{{2}} {{r}}}$;
${{{{ {\partial g}}_{\phi}}_{\phi}}_r} = {{{2}} {{r}} {{({{1} - {{cos\left( \theta\right)}^{2}}})}}}$;
${{{{ {\partial g}}_{\phi}}_{\phi}}_{\theta}} = {{{2}} {{{r}^{2}}} {{sin\left( \theta\right)}} {{cos\left( \theta\right)}}}$
1st kind Christoffel:
${{{{ \Gamma}_r}_{\theta}}_{\theta}} = {-{r}}$;
${{{{ \Gamma}_r}_{\phi}}_{\phi}} = {-{{{r}} {{({{1} - {{cos\left( \theta\right)}^{2}}})}}}}$;
${{{{ \Gamma}_{\theta}}_r}_{\theta}} = {r}$;
${{{{ \Gamma}_{\theta}}_{\theta}}_r} = {r}$;
${{{{ \Gamma}_{\theta}}_{\phi}}_{\phi}} = {-{{{{r}^{2}}} {{sin\left( \theta\right)}} {{cos\left( \theta\right)}}}}$;
${{{{ \Gamma}_{\phi}}_r}_{\phi}} = {{{r}} {{({{1} - {{cos\left( \theta\right)}^{2}}})}}}$;
${{{{ \Gamma}_{\phi}}_{\theta}}_{\phi}} = {{{{r}^{2}}} {{cos\left( \theta\right)}} {{sin\left( \theta\right)}}}$;
${{{{ \Gamma}_{\phi}}_{\phi}}_r} = {{{r}} {{({{1} - {{cos\left( \theta\right)}^{2}}})}}}$;
${{{{ \Gamma}_{\phi}}_{\phi}}_{\theta}} = {{{{r}^{2}}} {{cos\left( \theta\right)}} {{sin\left( \theta\right)}}}$
connection coefficients / 2nd kind Christoffel:
${{{{ \Gamma}^r}_{\theta}}_{\theta}} = {-{r}}$;
${{{{ \Gamma}^r}_{\phi}}_{\phi}} = {-{{{r}} {{({{1} - {{cos\left( \theta\right)}^{2}}})}}}}$;
${{{{ \Gamma}^{\theta}}_r}_{\theta}} = {{\frac{1}{r}}{({1})}}$;
${{{{ \Gamma}^{\theta}}_{\theta}}_r} = {{\frac{1}{r}}{({1})}}$;
${{{{ \Gamma}^{\theta}}_{\phi}}_{\phi}} = {-{{{cos\left( \theta\right)}} {{sin\left( \theta\right)}}}}$;
${{{{ \Gamma}^{\phi}}_r}_{\phi}} = {{\frac{1}{r}}{({1})}}$;
${{{{ \Gamma}^{\phi}}_{\theta}}_{\phi}} = {\frac{cos\left( \theta\right)}{sin\left( \theta\right)}}$;
${{{{ \Gamma}^{\phi}}_{\phi}}_r} = {{\frac{1}{r}}{({1})}}$;
${{{{ \Gamma}^{\phi}}_{\phi}}_{\theta}} = {\frac{cos\left( \theta\right)}{sin\left( \theta\right)}}$
connection coefficients derivative:
${{{{{ {\partial \Gamma}}^r}_{\theta}}_{\theta}}_r} = {-{1}}$;
${{{{{ {\partial \Gamma}}^r}_{\phi}}_{\phi}}_r} = {-{({{1} - {{cos\left( \theta\right)}^{2}}})}}$;
${{{{{ {\partial \Gamma}}^r}_{\phi}}_{\phi}}_{\theta}} = {-{{{2}} {{r}} {{cos\left( \theta\right)}} {{sin\left( \theta\right)}}}}$;
${{{{{ {\partial \Gamma}}^{\theta}}_r}_{\theta}}_r} = {-{\frac{1}{{r}^{2}}}}$;
${{{{{ {\partial \Gamma}}^{\theta}}_{\theta}}_r}_r} = {-{\frac{1}{{r}^{2}}}}$;
${{{{{ {\partial \Gamma}}^{\theta}}_{\phi}}_{\phi}}_{\theta}} = {{1} - {{{2}} {{{cos\left( \theta\right)}^{2}}}}}$;
${{{{{ {\partial \Gamma}}^{\phi}}_r}_{\phi}}_r} = {-{\frac{1}{{r}^{2}}}}$;
${{{{{ {\partial \Gamma}}^{\phi}}_{\theta}}_{\phi}}_{\theta}} = {-{\frac{1}{{1} - {{cos\left( \theta\right)}^{2}}}}}$;
${{{{{ {\partial \Gamma}}^{\phi}}_{\phi}}_r}_r} = {-{\frac{1}{{r}^{2}}}}$;
${{{{{ {\partial \Gamma}}^{\phi}}_{\phi}}_{\theta}}_{\theta}} = {-{\frac{1}{{1} - {{cos\left( \theta\right)}^{2}}}}}$
connection coefficients squared:
${{{{{ {(\Gamma^2)}}^r}_r}_{\theta}}_{\theta}} = {-{1}}$;
${{{{{ {(\Gamma^2)}}^r}_r}_{\phi}}_{\phi}} = {-{({{1} - {{cos\left( \theta\right)}^{2}}})}}$;
${{{{{ {(\Gamma^2)}}^r}_{\theta}}_{\theta}}_r} = {-{1}}$;
${{{{{ {(\Gamma^2)}}^r}_{\theta}}_{\phi}}_{\phi}} = {-{{{r}} {{cos\left( \theta\right)}} {{sin\left( \theta\right)}}}}$;
${{{{{ {(\Gamma^2)}}^r}_{\phi}}_{\theta}}_{\phi}} = {{{r}} {{cos\left( \theta\right)}} {{sin\left( \theta\right)}}}$;
${{{{{ {(\Gamma^2)}}^r}_{\phi}}_{\phi}}_r} = {-{({{1} - {{cos\left( \theta\right)}^{2}}})}}$;
${{{{{ {(\Gamma^2)}}^r}_{\phi}}_{\phi}}_{\theta}} = {-{{{r}} {{cos\left( \theta\right)}} {{sin\left( \theta\right)}}}}$;
${{{{{ {(\Gamma^2)}}^{\theta}}_r}_r}_{\theta}} = {\frac{1}{{r}^{2}}}$;
${{{{{ {(\Gamma^2)}}^{\theta}}_r}_{\phi}}_{\phi}} = {{\frac{1}{r}}{({-{{{cos\left( \theta\right)}} {{sin\left( \theta\right)}}}})}}$;
${{{{{ {(\Gamma^2)}}^{\theta}}_{\theta}}_r}_r} = {\frac{1}{{r}^{2}}}$;
${{{{{ {(\Gamma^2)}}^{\theta}}_{\theta}}_{\theta}}_{\theta}} = {-{1}}$;
${{{{{ {(\Gamma^2)}}^{\theta}}_{\theta}}_{\phi}}_{\phi}} = {-{{cos\left( \theta\right)}^{2}}}$;
${{{{{ {(\Gamma^2)}}^{\theta}}_{\phi}}_r}_{\phi}} = {{\frac{1}{r}}{({-{{{cos\left( \theta\right)}} {{sin\left( \theta\right)}}}})}}$;
${{{{{ {(\Gamma^2)}}^{\theta}}_{\phi}}_{\theta}}_{\phi}} = {-{({{1} - {{cos\left( \theta\right)}^{2}}})}}$;
${{{{{ {(\Gamma^2)}}^{\theta}}_{\phi}}_{\phi}}_r} = {{\frac{1}{r}}{({-{{{cos\left( \theta\right)}} {{sin\left( \theta\right)}}}})}}$;
${{{{{ {(\Gamma^2)}}^{\theta}}_{\phi}}_{\phi}}_{\theta}} = {-{{cos\left( \theta\right)}^{2}}}$;
${{{{{ {(\Gamma^2)}}^{\phi}}_r}_r}_{\phi}} = {\frac{1}{{r}^{2}}}$;
${{{{{ {(\Gamma^2)}}^{\phi}}_r}_{\theta}}_{\phi}} = {\frac{cos\left( \theta\right)}{{{r}} {{sin\left( \theta\right)}}}}$;
${{{{{ {(\Gamma^2)}}^{\phi}}_r}_{\phi}}_{\theta}} = {\frac{cos\left( \theta\right)}{{{r}} {{sin\left( \theta\right)}}}}$;
${{{{{ {(\Gamma^2)}}^{\phi}}_{\theta}}_r}_{\phi}} = {\frac{cos\left( \theta\right)}{{{r}} {{sin\left( \theta\right)}}}}$;
${{{{{ {(\Gamma^2)}}^{\phi}}_{\theta}}_{\theta}}_{\phi}} = {\frac{{cos\left( \theta\right)}^{2}}{{1} - {{cos\left( \theta\right)}^{2}}}}$;
${{{{{ {(\Gamma^2)}}^{\phi}}_{\theta}}_{\phi}}_r} = {\frac{cos\left( \theta\right)}{{{r}} {{sin\left( \theta\right)}}}}$;
${{{{{ {(\Gamma^2)}}^{\phi}}_{\theta}}_{\phi}}_{\theta}} = {-{1}}$;
${{{{{ {(\Gamma^2)}}^{\phi}}_{\phi}}_r}_r} = {\frac{1}{{r}^{2}}}$;
${{{{{ {(\Gamma^2)}}^{\phi}}_{\phi}}_r}_{\theta}} = {\frac{cos\left( \theta\right)}{{{r}} {{sin\left( \theta\right)}}}}$;
${{{{{ {(\Gamma^2)}}^{\phi}}_{\phi}}_{\theta}}_r} = {\frac{cos\left( \theta\right)}{{{r}} {{sin\left( \theta\right)}}}}$;
${{{{{ {(\Gamma^2)}}^{\phi}}_{\phi}}_{\theta}}_{\theta}} = {\frac{{cos\left( \theta\right)}^{2}}{{1} - {{cos\left( \theta\right)}^{2}}}}$;
${{{{{ {(\Gamma^2)}}^{\phi}}_{\phi}}_{\phi}}_{\phi}} = {-{1}}$
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: ${{{{ A}^i}_{,i}} + {{{{{{ \Gamma}^i}_i}_j}} {{{ A}^j}}}} = {{\frac{\partial {A^{t}}}{\partial t}} + {\frac{\partial {A^{r}}}{\partial r}} + {\frac{\partial {A^{\theta}}}{\partial \theta}} + {\frac{\partial {A^{\phi}}}{\partial \phi}} + {{{2}} {{{A^{r}}}} \cdot {{{\frac{1}{r}}{({1})}}}} + {{{{A^{\theta}}}} \cdot {{cos\left( \theta\right)}} {{\frac{1}{sin\left( \theta\right)}}}}}$
geodesic:
${\overset{a\downarrow}{\left[\begin{matrix} \ddot{t} \\ \ddot{r} \\ \ddot{\theta} \\ \ddot{\phi}\end{matrix}\right]}} = {\overset{a\downarrow}{\left[\begin{matrix} 0 \\ {{{r}} {{{\dot{\phi}}^{2}}}} + {{{-1}} {{r}} {{{\dot{\phi}}^{2}}} {{{cos\left( \theta\right)}^{2}}}} + {{{r}} {{{\dot{\theta}}^{2}}}} \\ {{{-2}} {{\dot{\theta}}} \cdot {{\dot{r}}} \cdot {{{\frac{1}{r}}{({1})}}}} + {{{r}} {{{\dot{\phi}}^{2}}} {{sin\left( \theta\right)}} {{cos\left( \theta\right)}} {{{\frac{1}{r}}{({1})}}}} \\ {{{-2}} {{\dot{\phi}}} \cdot {{\dot{\theta}}} \cdot {{r}} {{cos\left( \theta\right)}} {{{\frac{1}{r}}{({1})}}} {{\frac{1}{sin\left( \theta\right)}}}} + {{{-2}} {{\dot{\phi}}} \cdot {{\dot{r}}} \cdot {{sin\left( \theta\right)}} {{{\frac{1}{r}}{({1})}}} {{\frac{1}{sin\left( \theta\right)}}}}\end{matrix}\right]}}$
parallel propagators:
${{[\Gamma_t]}} = {\left[\begin{matrix} 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0\end{matrix}\right]}$
$\int\limits_{{{t_L}}}^{{{t_R}}}d t\left( \left[\begin{matrix} 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0\end{matrix}\right]\right)$
= $\left[\begin{matrix} 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0\end{matrix}\right]$
${ P}_t$ = ${ⅇ}^{( -{({\int\limits_{{{t_L}}}^{{{t_R}}}d t\left( \left[\begin{matrix} 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0\end{matrix}\right]\right)})})}$
= $\left[\begin{matrix} 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 1\end{matrix}\right]$
${{ P}_t}^{-1}$ = ${ⅇ}^{({\int\limits_{{{t_L}}}^{{{t_R}}}d t\left( \left[\begin{matrix} 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0\end{matrix}\right]\right)})}$
= $\left[\begin{matrix} 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 1\end{matrix}\right]$
${{[\Gamma_r]}} = {\left[\begin{matrix} 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 \\ 0 & 0 & {\frac{1}{r}}{({1})} & 0 \\ 0 & 0 & 0 & {\frac{1}{r}}{({1})}\end{matrix}\right]}$
$\int\limits_{{{r_L}}}^{{{r_R}}}d r\left( \left[\begin{matrix} 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 \\ 0 & 0 & {\frac{1}{r}}{({1})} & 0 \\ 0 & 0 & 0 & {\frac{1}{r}}{({1})}\end{matrix}\right]\right)$
= $\left[\begin{matrix} 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 \\ 0 & 0 & log\left( {{\frac{1}{{r_L}}}{({{r_R}})}}\right) & 0 \\ 0 & 0 & 0 & log\left( {{\frac{1}{{r_L}}}{({{r_R}})}}\right)\end{matrix}\right]$
${ P}_r$ = ${ⅇ}^{( -{({\int\limits_{{{r_L}}}^{{{r_R}}}d r\left( \left[\begin{matrix} 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 \\ 0 & 0 & {\frac{1}{r}}{({1})} & 0 \\ 0 & 0 & 0 & {\frac{1}{r}}{({1})}\end{matrix}\right]\right)})})}$
= $\left[\begin{matrix} 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & {\frac{1}{{r_R}}}{({{r_L}})} & 0 \\ 0 & 0 & 0 & {\frac{1}{{r_R}}}{({{r_L}})}\end{matrix}\right]$
${{ P}_r}^{-1}$ = ${ⅇ}^{({\int\limits_{{{r_L}}}^{{{r_R}}}d r\left( \left[\begin{matrix} 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 \\ 0 & 0 & {\frac{1}{r}}{({1})} & 0 \\ 0 & 0 & 0 & {\frac{1}{r}}{({1})}\end{matrix}\right]\right)})}$
= $\left[\begin{matrix} 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & {\frac{1}{{r_L}}}{({{r_R}})} & 0 \\ 0 & 0 & 0 & {\frac{1}{{r_L}}}{({{r_R}})}\end{matrix}\right]$
${{[\Gamma_\theta]}} = {\left[\begin{matrix} 0 & 0 & 0 & 0 \\ 0 & 0 & -{r} & 0 \\ 0 & {\frac{1}{r}}{({1})} & 0 & 0 \\ 0 & 0 & 0 & \frac{cos\left( \theta\right)}{sin\left( \theta\right)}\end{matrix}\right]}$
$\int\limits_{{{\theta_L}}}^{{{\theta_R}}}d \theta\left( \left[\begin{matrix} 0 & 0 & 0 & 0 \\ 0 & 0 & -{r} & 0 \\ 0 & {\frac{1}{r}}{({1})} & 0 & 0 \\ 0 & 0 & 0 & \frac{cos\left( \theta\right)}{sin\left( \theta\right)}\end{matrix}\right]\right)$
= $\left[\begin{matrix} 0 & 0 & 0 & 0 \\ 0 & 0 & {{r}} {{({{{\theta_L}} - {{\theta_R}}})}} & 0 \\ 0 & {\frac{1}{r}}{({-{({{{\theta_L}} - {{\theta_R}}})}})} & 0 & 0 \\ 0 & 0 & 0 & log\left( {\frac{|{sin\left( {\theta_R}\right)}|}{|{sin\left( {\theta_L}\right)}|}}\right)\end{matrix}\right]$
${ P}_{\theta}$ = ${ⅇ}^{( -{({\int\limits_{{{\theta_L}}}^{{{\theta_R}}}d \theta\left( \left[\begin{matrix} 0 & 0 & 0 & 0 \\ 0 & 0 & -{r} & 0 \\ 0 & {\frac{1}{r}}{({1})} & 0 & 0 \\ 0 & 0 & 0 & \frac{cos\left( \theta\right)}{sin\left( \theta\right)}\end{matrix}\right]\right)})})}$
= $\left[\begin{matrix} 1 & 0 & 0 & 0 \\ 0 & cos\left( {{{\theta_L}} - {{\theta_R}}}\right) & -{{{r}} {{sin\left( {{{\theta_L}} - {{\theta_R}}}\right)}}} & 0 \\ 0 & {\frac{1}{r}}{({sin\left( {{{\theta_L}} - {{\theta_R}}}\right)})} & cos\left( {{{\theta_L}} - {{\theta_R}}}\right) & 0 \\ 0 & 0 & 0 & \frac{|{sin\left( {\theta_L}\right)}|}{|{sin\left( {\theta_R}\right)}|}\end{matrix}\right]$
${{ P}_{\theta}}^{-1}$ = ${ⅇ}^{({\int\limits_{{{\theta_L}}}^{{{\theta_R}}}d \theta\left( \left[\begin{matrix} 0 & 0 & 0 & 0 \\ 0 & 0 & -{r} & 0 \\ 0 & {\frac{1}{r}}{({1})} & 0 & 0 \\ 0 & 0 & 0 & \frac{cos\left( \theta\right)}{sin\left( \theta\right)}\end{matrix}\right]\right)})}$
= $\left[\begin{matrix} 1 & 0 & 0 & 0 \\ 0 & cos\left( {{{\theta_L}} - {{\theta_R}}}\right) & {{r}} {{sin\left( {{{\theta_L}} - {{\theta_R}}}\right)}} & 0 \\ 0 & {\frac{1}{r}}{({-{sin\left( {{{\theta_L}} - {{\theta_R}}}\right)}})} & cos\left( {{{\theta_L}} - {{\theta_R}}}\right) & 0 \\ 0 & 0 & 0 & \frac{|{sin\left( {\theta_R}\right)}|}{|{sin\left( {\theta_L}\right)}|}\end{matrix}\right]$
${{[\Gamma_\phi]}} = {\left[\begin{matrix} 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & -{{{r}} {{({{1} - {{cos\left( \theta\right)}^{2}}})}}} \\ 0 & 0 & 0 & -{{{sin\left( \theta\right)}} {{cos\left( \theta\right)}}} \\ 0 & {\frac{1}{r}}{({1})} & \frac{cos\left( \theta\right)}{sin\left( \theta\right)} & 0\end{matrix}\right]}$
$\int\limits_{{{\phi_L}}}^{{{\phi_R}}}d \phi\left( \left[\begin{matrix} 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & -{{{r}} {{({{1} - {{cos\left( \theta\right)}^{2}}})}}} \\ 0 & 0 & 0 & -{{{sin\left( \theta\right)}} {{cos\left( \theta\right)}}} \\ 0 & {\frac{1}{r}}{({1})} & \frac{cos\left( \theta\right)}{sin\left( \theta\right)} & 0\end{matrix}\right]\right)$
= $\left[\begin{matrix} 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & {{r}} {{({{{{{\phi_L}} - {{{{\phi_L}}} \cdot {{{cos\left( \theta\right)}^{2}}}}} - {{\phi_R}}} + {{{{\phi_R}}} \cdot {{{cos\left( \theta\right)}^{2}}}}})}} \\ 0 & 0 & 0 & -{{{cos\left( \theta\right)}} {{sin\left( \theta\right)}} {{({{{\phi_R}} - {{\phi_L}}})}}} \\ 0 & {\frac{1}{r}}{({-{({{{\phi_L}} - {{\phi_R}}})}})} & \frac{-{{{cos\left( \theta\right)}} {{({{{\phi_L}} - {{\phi_R}}})}}}}{sin\left( \theta\right)} & 0\end{matrix}\right]$
${ P}_{\phi}$ = ${ⅇ}^{( -{({\int\limits_{{{\phi_L}}}^{{{\phi_R}}}d \phi\left( \left[\begin{matrix} 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & -{{{r}} {{({{1} - {{cos\left( \theta\right)}^{2}}})}}} \\ 0 & 0 & 0 & -{{{sin\left( \theta\right)}} {{cos\left( \theta\right)}}} \\ 0 & {\frac{1}{r}}{({1})} & \frac{cos\left( \theta\right)}{sin\left( \theta\right)} & 0\end{matrix}\right]\right)})})}$
= $\left[\begin{matrix} 1 & 0 & 0 & 0 \\ 0 & \frac{{{{{2}} {{{\phi_L}}} \cdot {{{cos\left( \theta\right)}^{2}}}} - {{{2}} {{{\phi_R}}} \cdot {{{cos\left( \theta\right)}^{2}}}}} + {{{{{{\phi_L}}} \cdot {{\frac{1}{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}}}} - {{{{\phi_L}}} \cdot {{\frac{1}{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}}} {{{cos\left( \theta\right)}^{2}}}}} - {{{{\phi_R}}} \cdot {{\frac{1}{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}}}}} + {{{{\phi_R}}} \cdot {{\frac{1}{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}}} {{{cos\left( \theta\right)}^{2}}}} + {{{{{{\phi_L}}} \cdot {{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}}} - {{{{\phi_L}}} \cdot {{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}} {{{cos\left( \theta\right)}^{2}}}}} - {{{{\phi_R}}} \cdot {{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}}}} + {{{{\phi_R}}} \cdot {{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}} {{{cos\left( \theta\right)}^{2}}}}}{{{2}} {{({{{\phi_L}} - {{\phi_R}}})}}} & \frac{-{{{r}} {{sin\left( \theta\right)}} {{cos\left( \theta\right)}} {{({{{{{{{2}} {{{\phi_L}}}} - {{{{\phi_L}}} \cdot {{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}}}} - {{{{\phi_L}}} \cdot {{\frac{1}{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}}}}} - {{{2}} {{{\phi_R}}}}} + {{{{\phi_R}}} \cdot {{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}}} + {{{{\phi_R}}} \cdot {{\frac{1}{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}}}}})}}}}{{{2}} {{({{{\phi_L}} - {{\phi_R}}})}}} & \frac{{{r}} {{\frac{1}{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}}} {{({{{{\phi_L}} - {{{{\phi_L}}} \cdot {{{ⅇ}^{({{{2}} {{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}})}}}}} + {{{{{{\phi_L}}} \cdot {{{ⅇ}^{({{{2}} {{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}})}}} {{{cos\left( \theta\right)}^{2}}}} - {{{{\phi_L}}} \cdot {{{cos\left( \theta\right)}^{2}}}}} - {{\phi_R}}} + {{{{{\phi_R}}} \cdot {{{ⅇ}^{({{{2}} {{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}})}}}} - {{{{\phi_R}}} \cdot {{{ⅇ}^{({{{2}} {{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}})}}} {{{cos\left( \theta\right)}^{2}}}}} + {{{{\phi_R}}} \cdot {{{cos\left( \theta\right)}^{2}}}}})}}}{{{2}} {{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}} \\ 0 & \frac{{{cos\left( \theta\right)}} {{sin\left( \theta\right)}} {{({{{2} - {{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}} - {\frac{1}{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}}})}}}{-{{{2}} {{r}}}} & {\frac{1}{2}}{({{{2} - {{{2}} {{{cos\left( \theta\right)}^{2}}}}} + {{{\frac{1}{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}}} {{{cos\left( \theta\right)}^{2}}}} + {{{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}} {{{cos\left( \theta\right)}^{2}}}}})} & \frac{-{{{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}} {{cos\left( \theta\right)}} {{sin\left( \theta\right)}} {{({{{{{\phi_L}} - {{\phi_R}}} - {{{{\phi_L}}} \cdot {{\frac{1}{{ⅇ}^{({{{2}} {{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}})}}}}}} + {{{{\phi_R}}} \cdot {{\frac{1}{{ⅇ}^{({{{2}} {{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}})}}}}}})}}}}{{{2}} {{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}} \\ 0 & \frac{{{\frac{1}{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}}} {{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}} {{({{1} - {{ⅇ}^{({{{2}} {{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}})}}})}}}{{{2}} {{r}} {{({{{\phi_L}} - {{\phi_R}}})}}} & \frac{{{\frac{1}{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}}} {{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}} {{cos\left( \theta\right)}} {{({{1} - {{ⅇ}^{({{{2}} {{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}})}}})}}}{{{2}} {{sin\left( \theta\right)}} {{({{{\phi_L}} - {{\phi_R}}})}}} & {\frac{1}{2}}{({{{\frac{1}{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}}} {{({{1} + {{ⅇ}^{({{{2}} {{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}})}}})}}})}\end{matrix}\right]$
${{ P}_{\phi}}^{-1}$ = ${ⅇ}^{({\int\limits_{{{\phi_L}}}^{{{\phi_R}}}d \phi\left( \left[\begin{matrix} 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & -{{{r}} {{({{1} - {{cos\left( \theta\right)}^{2}}})}}} \\ 0 & 0 & 0 & -{{{sin\left( \theta\right)}} {{cos\left( \theta\right)}}} \\ 0 & {\frac{1}{r}}{({1})} & \frac{cos\left( \theta\right)}{sin\left( \theta\right)} & 0\end{matrix}\right]\right)})}$
= $\left[\begin{matrix} 1 & 0 & 0 & 0 \\ 0 & \frac{{{{{2}} {{{\phi_L}}} \cdot {{{cos\left( \theta\right)}^{2}}}} - {{{2}} {{{\phi_R}}} \cdot {{{cos\left( \theta\right)}^{2}}}}} + {{{{{{\phi_L}}} \cdot {{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}}} - {{{{\phi_L}}} \cdot {{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}} {{{cos\left( \theta\right)}^{2}}}}} - {{{{\phi_R}}} \cdot {{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}}}} + {{{{\phi_R}}} \cdot {{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}} {{{cos\left( \theta\right)}^{2}}}} + {{{{{{\phi_L}}} \cdot {{\frac{1}{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}}}} - {{{{\phi_L}}} \cdot {{\frac{1}{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}}} {{{cos\left( \theta\right)}^{2}}}}} - {{{{\phi_R}}} \cdot {{\frac{1}{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}}}}} + {{{{\phi_R}}} \cdot {{\frac{1}{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}}} {{{cos\left( \theta\right)}^{2}}}}}{{{2}} {{({{{\phi_L}} - {{\phi_R}}})}}} & \frac{-{{{r}} {{sin\left( \theta\right)}} {{cos\left( \theta\right)}} {{({{{{{{{2}} {{{\phi_L}}}} - {{{{\phi_L}}} \cdot {{\frac{1}{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}}}}} - {{{{\phi_L}}} \cdot {{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}}}} - {{{2}} {{{\phi_R}}}}} + {{{{\phi_R}}} \cdot {{\frac{1}{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}}}} + {{{{\phi_R}}} \cdot {{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}}}})}}}}{{{2}} {{({{{\phi_L}} - {{\phi_R}}})}}} & \frac{{{r}} {{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}} {{({{{{\phi_L}} - {{{{\phi_L}}} \cdot {{\frac{1}{{ⅇ}^{({{{2}} {{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}})}}}}}} + {{{{{{\phi_L}}} \cdot {{\frac{1}{{ⅇ}^{({{{2}} {{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}})}}}} {{{cos\left( \theta\right)}^{2}}}} - {{{{\phi_L}}} \cdot {{{cos\left( \theta\right)}^{2}}}}} - {{\phi_R}}} + {{{{{\phi_R}}} \cdot {{\frac{1}{{ⅇ}^{({{{2}} {{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}})}}}}} - {{{{\phi_R}}} \cdot {{\frac{1}{{ⅇ}^{({{{2}} {{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}})}}}} {{{cos\left( \theta\right)}^{2}}}}} + {{{{\phi_R}}} \cdot {{{cos\left( \theta\right)}^{2}}}}})}}}{{{2}} {{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}} \\ 0 & \frac{{{cos\left( \theta\right)}} {{sin\left( \theta\right)}} {{({{{2} - {\frac{1}{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}}} - {{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}})}}}{-{{{2}} {{r}}}} & {\frac{1}{2}}{({{{2} - {{{2}} {{{cos\left( \theta\right)}^{2}}}}} + {{{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}} {{{cos\left( \theta\right)}^{2}}}} + {{{\frac{1}{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}}} {{{cos\left( \theta\right)}^{2}}}}})} & \frac{-{{{\frac{1}{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}}} {{cos\left( \theta\right)}} {{sin\left( \theta\right)}} {{({{{{{\phi_L}} - {{\phi_R}}} - {{{{\phi_L}}} \cdot {{{ⅇ}^{({{{2}} {{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}})}}}}} + {{{{\phi_R}}} \cdot {{{ⅇ}^{({{{2}} {{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}})}}}}})}}}}{{{2}} {{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}} \\ 0 & \frac{{{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}} {{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}} {{({{1} - {\frac{1}{{ⅇ}^{({{{2}} {{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}})}}}})}}}{{{2}} {{r}} {{({{{\phi_L}} - {{\phi_R}}})}}} & \frac{{{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}} {{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}} {{cos\left( \theta\right)}} {{({{1} - {\frac{1}{{ⅇ}^{({{{2}} {{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}})}}}})}}}{{{2}} {{sin\left( \theta\right)}} {{({{{\phi_L}} - {{\phi_R}}})}}} & {\frac{1}{2}}{({{{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}} {{({{1} + {\frac{1}{{ⅇ}^{({{{2}} {{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}})}}}})}}})}\end{matrix}\right]$
propagator commutation:
[ ${ P}_t$ , ${ P}_r$ ] = ${ {\left[\begin{matrix} 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 1\end{matrix}\right]} {\left[\begin{matrix} 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & {\frac{1}{{r_R}}}{({{r_L}})} & 0 \\ 0 & 0 & 0 & {\frac{1}{{r_R}}}{({{r_L}})}\end{matrix}\right]}} - { {\left[\begin{matrix} 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & {\frac{1}{{r_R}}}{({{r_L}})} & 0 \\ 0 & 0 & 0 & {\frac{1}{{r_R}}}{({{r_L}})}\end{matrix}\right]} {\left[\begin{matrix} 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 1\end{matrix}\right]}}$ = $\left[\begin{matrix} 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0\end{matrix}\right]$
[ ${ P}_t$ , ${ P}_{\theta}$ ] = ${ {\left[\begin{matrix} 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 1\end{matrix}\right]} {\left[\begin{matrix} 1 & 0 & 0 & 0 \\ 0 & cos\left( {{{\theta_L}} - {{\theta_R}}}\right) & -{{{sin\left( {{{\theta_L}} - {{\theta_R}}}\right)}} {{{r_L}}}} & 0 \\ 0 & {\frac{1}{{r_L}}}{({sin\left( {{{\theta_L}} - {{\theta_R}}}\right)})} & cos\left( {{{\theta_L}} - {{\theta_R}}}\right) & 0 \\ 0 & 0 & 0 & \frac{|{sin\left( {\theta_L}\right)}|}{|{sin\left( {\theta_R}\right)}|}\end{matrix}\right]}} - { {\left[\begin{matrix} 1 & 0 & 0 & 0 \\ 0 & cos\left( {{{\theta_L}} - {{\theta_R}}}\right) & -{{{sin\left( {{{\theta_L}} - {{\theta_R}}}\right)}} {{{r_L}}}} & 0 \\ 0 & {\frac{1}{{r_L}}}{({sin\left( {{{\theta_L}} - {{\theta_R}}}\right)})} & cos\left( {{{\theta_L}} - {{\theta_R}}}\right) & 0 \\ 0 & 0 & 0 & \frac{|{sin\left( {\theta_L}\right)}|}{|{sin\left( {\theta_R}\right)}|}\end{matrix}\right]} {\left[\begin{matrix} 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 1\end{matrix}\right]}}$ = $\left[\begin{matrix} 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0\end{matrix}\right]$
[ ${ P}_t$ , ${ P}_{\phi}$ ] = ${ {\left[\begin{matrix} 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 1\end{matrix}\right]} {\left[\begin{matrix} 1 & 0 & 0 & 0 \\ 0 & \frac{{{{{2}} {{{\phi_L}}} \cdot {{{cos\left( {\theta_L}\right)}^{2}}}} - {{{2}} {{{\phi_R}}} \cdot {{{cos\left( {\theta_L}\right)}^{2}}}}} + {{{{{{\phi_L}}} \cdot {{\frac{1}{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}}}} - {{{{\phi_L}}} \cdot {{\frac{1}{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}}} {{{cos\left( {\theta_L}\right)}^{2}}}}} - {{{{\phi_R}}} \cdot {{\frac{1}{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}}}}} + {{{{\phi_R}}} \cdot {{\frac{1}{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}}} {{{cos\left( {\theta_L}\right)}^{2}}}} + {{{{{{\phi_L}}} \cdot {{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}}} - {{{{\phi_L}}} \cdot {{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}} {{{cos\left( {\theta_L}\right)}^{2}}}}} - {{{{\phi_R}}} \cdot {{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}}}} + {{{{\phi_R}}} \cdot {{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}} {{{cos\left( {\theta_L}\right)}^{2}}}}}{{{2}} {{({{{\phi_L}} - {{\phi_R}}})}}} & \frac{-{{{sin\left( {\theta_L}\right)}} {{cos\left( {\theta_L}\right)}} {{({{{{{{{2}} {{{\phi_L}}}} - {{{{\phi_L}}} \cdot {{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}}}} - {{{{\phi_L}}} \cdot {{\frac{1}{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}}}}} - {{{2}} {{{\phi_R}}}}} + {{{{\phi_R}}} \cdot {{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}}} + {{{{\phi_R}}} \cdot {{\frac{1}{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}}}}})}} {{{r_L}}}}}{{{2}} {{({{{\phi_L}} - {{\phi_R}}})}}} & \frac{{{\frac{1}{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}}} {{({{{{\phi_L}} - {{{{\phi_L}}} \cdot {{{ⅇ}^{({{{2}} {{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}})}}}}} + {{{{{{\phi_L}}} \cdot {{{ⅇ}^{({{{2}} {{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}})}}} {{{cos\left( {\theta_L}\right)}^{2}}}} - {{{{\phi_L}}} \cdot {{{cos\left( {\theta_L}\right)}^{2}}}}} - {{\phi_R}}} + {{{{{\phi_R}}} \cdot {{{ⅇ}^{({{{2}} {{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}})}}}} - {{{{\phi_R}}} \cdot {{{ⅇ}^{({{{2}} {{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}})}}} {{{cos\left( {\theta_L}\right)}^{2}}}}} + {{{{\phi_R}}} \cdot {{{cos\left( {\theta_L}\right)}^{2}}}}})}} {{{r_L}}}}{{{2}} {{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}} \\ 0 & \frac{{{cos\left( {\theta_L}\right)}} {{sin\left( {\theta_L}\right)}} {{({{{2} - {{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}} - {\frac{1}{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}}})}}}{-{{{2}} {{{r_L}}}}} & {\frac{1}{2}}{({{{2} - {{{2}} {{{cos\left( {\theta_L}\right)}^{2}}}}} + {{{\frac{1}{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}}} {{{cos\left( {\theta_L}\right)}^{2}}}} + {{{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}} {{{cos\left( {\theta_L}\right)}^{2}}}}})} & \frac{-{{{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}} {{cos\left( {\theta_L}\right)}} {{sin\left( {\theta_L}\right)}} {{({{{{{\phi_L}} - {{\phi_R}}} - {{{{\phi_L}}} \cdot {{\frac{1}{{ⅇ}^{({{{2}} {{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}})}}}}}} + {{{{\phi_R}}} \cdot {{\frac{1}{{ⅇ}^{({{{2}} {{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}})}}}}}})}}}}{{{2}} {{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}} \\ 0 & \frac{{{\frac{1}{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}}} {{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}} {{({{1} - {{ⅇ}^{({{{2}} {{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}})}}})}}}{{{2}} {{({{{\phi_L}} - {{\phi_R}}})}} {{{r_L}}}} & \frac{{{\frac{1}{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}}} {{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}} {{cos\left( {\theta_L}\right)}} {{({{1} - {{ⅇ}^{({{{2}} {{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}})}}})}}}{{{2}} {{sin\left( {\theta_L}\right)}} {{({{{\phi_L}} - {{\phi_R}}})}}} & {\frac{1}{2}}{({{{\frac{1}{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}}} {{({{1} + {{ⅇ}^{({{{2}} {{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}})}}})}}})}\end{matrix}\right]}} - { {\left[\begin{matrix} 1 & 0 & 0 & 0 \\ 0 & \frac{{{{{2}} {{{\phi_L}}} \cdot {{{cos\left( {\theta_L}\right)}^{2}}}} - {{{2}} {{{\phi_R}}} \cdot {{{cos\left( {\theta_L}\right)}^{2}}}}} + {{{{{{\phi_L}}} \cdot {{\frac{1}{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}}}} - {{{{\phi_L}}} \cdot {{\frac{1}{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}}} {{{cos\left( {\theta_L}\right)}^{2}}}}} - {{{{\phi_R}}} \cdot {{\frac{1}{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}}}}} + {{{{\phi_R}}} \cdot {{\frac{1}{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}}} {{{cos\left( {\theta_L}\right)}^{2}}}} + {{{{{{\phi_L}}} \cdot {{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}}} - {{{{\phi_L}}} \cdot {{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}} {{{cos\left( {\theta_L}\right)}^{2}}}}} - {{{{\phi_R}}} \cdot {{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}}}} + {{{{\phi_R}}} \cdot {{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}} {{{cos\left( {\theta_L}\right)}^{2}}}}}{{{2}} {{({{{\phi_L}} - {{\phi_R}}})}}} & \frac{-{{{sin\left( {\theta_L}\right)}} {{cos\left( {\theta_L}\right)}} {{({{{{{{{2}} {{{\phi_L}}}} - {{{{\phi_L}}} \cdot {{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}}}} - {{{{\phi_L}}} \cdot {{\frac{1}{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}}}}} - {{{2}} {{{\phi_R}}}}} + {{{{\phi_R}}} \cdot {{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}}} + {{{{\phi_R}}} \cdot {{\frac{1}{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}}}}})}} {{{r_L}}}}}{{{2}} {{({{{\phi_L}} - {{\phi_R}}})}}} & \frac{{{\frac{1}{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}}} {{({{{{\phi_L}} - {{{{\phi_L}}} \cdot {{{ⅇ}^{({{{2}} {{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}})}}}}} + {{{{{{\phi_L}}} \cdot {{{ⅇ}^{({{{2}} {{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}})}}} {{{cos\left( {\theta_L}\right)}^{2}}}} - {{{{\phi_L}}} \cdot {{{cos\left( {\theta_L}\right)}^{2}}}}} - {{\phi_R}}} + {{{{{\phi_R}}} \cdot {{{ⅇ}^{({{{2}} {{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}})}}}} - {{{{\phi_R}}} \cdot {{{ⅇ}^{({{{2}} {{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}})}}} {{{cos\left( {\theta_L}\right)}^{2}}}}} + {{{{\phi_R}}} \cdot {{{cos\left( {\theta_L}\right)}^{2}}}}})}} {{{r_L}}}}{{{2}} {{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}} \\ 0 & \frac{{{cos\left( {\theta_L}\right)}} {{sin\left( {\theta_L}\right)}} {{({{{2} - {{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}} - {\frac{1}{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}}})}}}{-{{{2}} {{{r_L}}}}} & {\frac{1}{2}}{({{{2} - {{{2}} {{{cos\left( {\theta_L}\right)}^{2}}}}} + {{{\frac{1}{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}}} {{{cos\left( {\theta_L}\right)}^{2}}}} + {{{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}} {{{cos\left( {\theta_L}\right)}^{2}}}}})} & \frac{-{{{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}} {{cos\left( {\theta_L}\right)}} {{sin\left( {\theta_L}\right)}} {{({{{{{\phi_L}} - {{\phi_R}}} - {{{{\phi_L}}} \cdot {{\frac{1}{{ⅇ}^{({{{2}} {{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}})}}}}}} + {{{{\phi_R}}} \cdot {{\frac{1}{{ⅇ}^{({{{2}} {{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}})}}}}}})}}}}{{{2}} {{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}} \\ 0 & \frac{{{\frac{1}{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}}} {{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}} {{({{1} - {{ⅇ}^{({{{2}} {{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}})}}})}}}{{{2}} {{({{{\phi_L}} - {{\phi_R}}})}} {{{r_L}}}} & \frac{{{\frac{1}{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}}} {{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}} {{cos\left( {\theta_L}\right)}} {{({{1} - {{ⅇ}^{({{{2}} {{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}})}}})}}}{{{2}} {{sin\left( {\theta_L}\right)}} {{({{{\phi_L}} - {{\phi_R}}})}}} & {\frac{1}{2}}{({{{\frac{1}{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}}} {{({{1} + {{ⅇ}^{({{{2}} {{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}})}}})}}})}\end{matrix}\right]} {\left[\begin{matrix} 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 1\end{matrix}\right]}}$ = $\left[\begin{matrix} 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0\end{matrix}\right]$
[ ${ P}_r$ , ${ P}_{\theta}$ ] = ${ {\left[\begin{matrix} 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & {\frac{1}{{r_R}}}{({{r_L}})} & 0 \\ 0 & 0 & 0 & {\frac{1}{{r_R}}}{({{r_L}})}\end{matrix}\right]} {\left[\begin{matrix} 1 & 0 & 0 & 0 \\ 0 & cos\left( {{{\theta_L}} - {{\theta_R}}}\right) & -{{{sin\left( {{{\theta_L}} - {{\theta_R}}}\right)}} {{{r_L}}}} & 0 \\ 0 & {\frac{1}{{r_L}}}{({sin\left( {{{\theta_L}} - {{\theta_R}}}\right)})} & cos\left( {{{\theta_L}} - {{\theta_R}}}\right) & 0 \\ 0 & 0 & 0 & \frac{|{sin\left( {\theta_L}\right)}|}{|{sin\left( {\theta_R}\right)}|}\end{matrix}\right]}} - { {\left[\begin{matrix} 1 & 0 & 0 & 0 \\ 0 & cos\left( {{{\theta_L}} - {{\theta_R}}}\right) & -{{{sin\left( {{{\theta_L}} - {{\theta_R}}}\right)}} {{{r_R}}}} & 0 \\ 0 & {\frac{1}{{r_R}}}{({sin\left( {{{\theta_L}} - {{\theta_R}}}\right)})} & cos\left( {{{\theta_L}} - {{\theta_R}}}\right) & 0 \\ 0 & 0 & 0 & \frac{|{sin\left( {\theta_L}\right)}|}{|{sin\left( {\theta_R}\right)}|}\end{matrix}\right]} {\left[\begin{matrix} 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & {\frac{1}{{r_R}}}{({{r_L}})} & 0 \\ 0 & 0 & 0 & {\frac{1}{{r_R}}}{({{r_L}})}\end{matrix}\right]}}$ = $\left[\begin{matrix} 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0\end{matrix}\right]$
[ ${ P}_r$ , ${ P}_{\phi}$ ] = ${ {\left[\begin{matrix} 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & {\frac{1}{{r_R}}}{({{r_L}})} & 0 \\ 0 & 0 & 0 & {\frac{1}{{r_R}}}{({{r_L}})}\end{matrix}\right]} {\left[\begin{matrix} 1 & 0 & 0 & 0 \\ 0 & \frac{{{{{2}} {{{\phi_L}}} \cdot {{{cos\left( {\theta_L}\right)}^{2}}}} - {{{2}} {{{\phi_R}}} \cdot {{{cos\left( {\theta_L}\right)}^{2}}}}} + {{{{{{\phi_L}}} \cdot {{\frac{1}{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}}}} - {{{{\phi_L}}} \cdot {{\frac{1}{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}}} {{{cos\left( {\theta_L}\right)}^{2}}}}} - {{{{\phi_R}}} \cdot {{\frac{1}{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}}}}} + {{{{\phi_R}}} \cdot {{\frac{1}{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}}} {{{cos\left( {\theta_L}\right)}^{2}}}} + {{{{{{\phi_L}}} \cdot {{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}}} - {{{{\phi_L}}} \cdot {{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}} {{{cos\left( {\theta_L}\right)}^{2}}}}} - {{{{\phi_R}}} \cdot {{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}}}} + {{{{\phi_R}}} \cdot {{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}} {{{cos\left( {\theta_L}\right)}^{2}}}}}{{{2}} {{({{{\phi_L}} - {{\phi_R}}})}}} & \frac{-{{{sin\left( {\theta_L}\right)}} {{cos\left( {\theta_L}\right)}} {{({{{{{{{2}} {{{\phi_L}}}} - {{{{\phi_L}}} \cdot {{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}}}} - {{{{\phi_L}}} \cdot {{\frac{1}{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}}}}} - {{{2}} {{{\phi_R}}}}} + {{{{\phi_R}}} \cdot {{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}}} + {{{{\phi_R}}} \cdot {{\frac{1}{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}}}}})}} {{{r_L}}}}}{{{2}} {{({{{\phi_L}} - {{\phi_R}}})}}} & \frac{{{\frac{1}{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}}} {{({{{{\phi_L}} - {{{{\phi_L}}} \cdot {{{ⅇ}^{({{{2}} {{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}})}}}}} + {{{{{{\phi_L}}} \cdot {{{ⅇ}^{({{{2}} {{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}})}}} {{{cos\left( {\theta_L}\right)}^{2}}}} - {{{{\phi_L}}} \cdot {{{cos\left( {\theta_L}\right)}^{2}}}}} - {{\phi_R}}} + {{{{{\phi_R}}} \cdot {{{ⅇ}^{({{{2}} {{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}})}}}} - {{{{\phi_R}}} \cdot {{{ⅇ}^{({{{2}} {{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}})}}} {{{cos\left( {\theta_L}\right)}^{2}}}}} + {{{{\phi_R}}} \cdot {{{cos\left( {\theta_L}\right)}^{2}}}}})}} {{{r_L}}}}{{{2}} {{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}} \\ 0 & \frac{{{cos\left( {\theta_L}\right)}} {{sin\left( {\theta_L}\right)}} {{({{{2} - {{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}} - {\frac{1}{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}}})}}}{-{{{2}} {{{r_L}}}}} & {\frac{1}{2}}{({{{2} - {{{2}} {{{cos\left( {\theta_L}\right)}^{2}}}}} + {{{\frac{1}{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}}} {{{cos\left( {\theta_L}\right)}^{2}}}} + {{{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}} {{{cos\left( {\theta_L}\right)}^{2}}}}})} & \frac{-{{{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}} {{cos\left( {\theta_L}\right)}} {{sin\left( {\theta_L}\right)}} {{({{{{{\phi_L}} - {{\phi_R}}} - {{{{\phi_L}}} \cdot {{\frac{1}{{ⅇ}^{({{{2}} {{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}})}}}}}} + {{{{\phi_R}}} \cdot {{\frac{1}{{ⅇ}^{({{{2}} {{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}})}}}}}})}}}}{{{2}} {{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}} \\ 0 & \frac{{{\frac{1}{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}}} {{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}} {{({{1} - {{ⅇ}^{({{{2}} {{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}})}}})}}}{{{2}} {{({{{\phi_L}} - {{\phi_R}}})}} {{{r_L}}}} & \frac{{{\frac{1}{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}}} {{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}} {{cos\left( {\theta_L}\right)}} {{({{1} - {{ⅇ}^{({{{2}} {{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}})}}})}}}{{{2}} {{sin\left( {\theta_L}\right)}} {{({{{\phi_L}} - {{\phi_R}}})}}} & {\frac{1}{2}}{({{{\frac{1}{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}}} {{({{1} + {{ⅇ}^{({{{2}} {{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}})}}})}}})}\end{matrix}\right]}} - { {\left[\begin{matrix} 1 & 0 & 0 & 0 \\ 0 & \frac{{{{{2}} {{{\phi_L}}} \cdot {{{cos\left( {\theta_L}\right)}^{2}}}} - {{{2}} {{{\phi_R}}} \cdot {{{cos\left( {\theta_L}\right)}^{2}}}}} + {{{{{{\phi_L}}} \cdot {{\frac{1}{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}}}} - {{{{\phi_L}}} \cdot {{\frac{1}{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}}} {{{cos\left( {\theta_L}\right)}^{2}}}}} - {{{{\phi_R}}} \cdot {{\frac{1}{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}}}}} + {{{{\phi_R}}} \cdot {{\frac{1}{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}}} {{{cos\left( {\theta_L}\right)}^{2}}}} + {{{{{{\phi_L}}} \cdot {{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}}} - {{{{\phi_L}}} \cdot {{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}} {{{cos\left( {\theta_L}\right)}^{2}}}}} - {{{{\phi_R}}} \cdot {{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}}}} + {{{{\phi_R}}} \cdot {{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}} {{{cos\left( {\theta_L}\right)}^{2}}}}}{{{2}} {{({{{\phi_L}} - {{\phi_R}}})}}} & \frac{-{{{sin\left( {\theta_L}\right)}} {{cos\left( {\theta_L}\right)}} {{({{{{{{{2}} {{{\phi_L}}}} - {{{{\phi_L}}} \cdot {{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}}}} - {{{{\phi_L}}} \cdot {{\frac{1}{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}}}}} - {{{2}} {{{\phi_R}}}}} + {{{{\phi_R}}} \cdot {{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}}} + {{{{\phi_R}}} \cdot {{\frac{1}{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}}}}})}} {{{r_R}}}}}{{{2}} {{({{{\phi_L}} - {{\phi_R}}})}}} & \frac{{{\frac{1}{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}}} {{({{{{\phi_L}} - {{{{\phi_L}}} \cdot {{{ⅇ}^{({{{2}} {{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}})}}}}} + {{{{{{\phi_L}}} \cdot {{{ⅇ}^{({{{2}} {{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}})}}} {{{cos\left( {\theta_L}\right)}^{2}}}} - {{{{\phi_L}}} \cdot {{{cos\left( {\theta_L}\right)}^{2}}}}} - {{\phi_R}}} + {{{{{\phi_R}}} \cdot {{{ⅇ}^{({{{2}} {{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}})}}}} - {{{{\phi_R}}} \cdot {{{ⅇ}^{({{{2}} {{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}})}}} {{{cos\left( {\theta_L}\right)}^{2}}}}} + {{{{\phi_R}}} \cdot {{{cos\left( {\theta_L}\right)}^{2}}}}})}} {{{r_R}}}}{{{2}} {{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}} \\ 0 & \frac{{{cos\left( {\theta_L}\right)}} {{sin\left( {\theta_L}\right)}} {{({{{2} - {{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}} - {\frac{1}{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}}})}}}{-{{{2}} {{{r_R}}}}} & {\frac{1}{2}}{({{{2} - {{{2}} {{{cos\left( {\theta_L}\right)}^{2}}}}} + {{{\frac{1}{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}}} {{{cos\left( {\theta_L}\right)}^{2}}}} + {{{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}} {{{cos\left( {\theta_L}\right)}^{2}}}}})} & \frac{-{{{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}} {{cos\left( {\theta_L}\right)}} {{sin\left( {\theta_L}\right)}} {{({{{{{\phi_L}} - {{\phi_R}}} - {{{{\phi_L}}} \cdot {{\frac{1}{{ⅇ}^{({{{2}} {{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}})}}}}}} + {{{{\phi_R}}} \cdot {{\frac{1}{{ⅇ}^{({{{2}} {{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}})}}}}}})}}}}{{{2}} {{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}} \\ 0 & \frac{{{\frac{1}{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}}} {{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}} {{({{1} - {{ⅇ}^{({{{2}} {{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}})}}})}}}{{{2}} {{({{{\phi_L}} - {{\phi_R}}})}} {{{r_R}}}} & \frac{{{\frac{1}{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}}} {{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}} {{cos\left( {\theta_L}\right)}} {{({{1} - {{ⅇ}^{({{{2}} {{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}})}}})}}}{{{2}} {{sin\left( {\theta_L}\right)}} {{({{{\phi_L}} - {{\phi_R}}})}}} & {\frac{1}{2}}{({{{\frac{1}{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}}} {{({{1} + {{ⅇ}^{({{{2}} {{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}})}}})}}})}\end{matrix}\right]} {\left[\begin{matrix} 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & {\frac{1}{{r_R}}}{({{r_L}})} & 0 \\ 0 & 0 & 0 & {\frac{1}{{r_R}}}{({{r_L}})}\end{matrix}\right]}}$ = $\left[\begin{matrix} 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0\end{matrix}\right]$
[ ${ P}_{\theta}$ , ${ P}_{\phi}$ ] = ${ {\left[\begin{matrix} 1 & 0 & 0 & 0 \\ 0 & cos\left( {{{\theta_L}} - {{\theta_R}}}\right) & -{{{sin\left( {{{\theta_L}} - {{\theta_R}}}\right)}} {{{r_L}}}} & 0 \\ 0 & {\frac{1}{{r_L}}}{({sin\left( {{{\theta_L}} - {{\theta_R}}}\right)})} & cos\left( {{{\theta_L}} - {{\theta_R}}}\right) & 0 \\ 0 & 0 & 0 & \frac{|{sin\left( {\theta_L}\right)}|}{|{sin\left( {\theta_R}\right)}|}\end{matrix}\right]} {\left[\begin{matrix} 1 & 0 & 0 & 0 \\ 0 & \frac{{{{{2}} {{{\phi_L}}} \cdot {{{cos\left( {\theta_L}\right)}^{2}}}} - {{{2}} {{{\phi_R}}} \cdot {{{cos\left( {\theta_L}\right)}^{2}}}}} + {{{{{{\phi_L}}} \cdot {{\frac{1}{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}}}} - {{{{\phi_L}}} \cdot {{\frac{1}{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}}} {{{cos\left( {\theta_L}\right)}^{2}}}}} - {{{{\phi_R}}} \cdot {{\frac{1}{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}}}}} + {{{{\phi_R}}} \cdot {{\frac{1}{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}}} {{{cos\left( {\theta_L}\right)}^{2}}}} + {{{{{{\phi_L}}} \cdot {{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}}} - {{{{\phi_L}}} \cdot {{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}} {{{cos\left( {\theta_L}\right)}^{2}}}}} - {{{{\phi_R}}} \cdot {{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}}}} + {{{{\phi_R}}} \cdot {{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}} {{{cos\left( {\theta_L}\right)}^{2}}}}}{{{2}} {{({{{\phi_L}} - {{\phi_R}}})}}} & \frac{-{{{sin\left( {\theta_L}\right)}} {{cos\left( {\theta_L}\right)}} {{({{{{{{{2}} {{{\phi_L}}}} - {{{{\phi_L}}} \cdot {{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}}}} - {{{{\phi_L}}} \cdot {{\frac{1}{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}}}}} - {{{2}} {{{\phi_R}}}}} + {{{{\phi_R}}} \cdot {{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}}} + {{{{\phi_R}}} \cdot {{\frac{1}{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}}}}})}} {{{r_L}}}}}{{{2}} {{({{{\phi_L}} - {{\phi_R}}})}}} & \frac{{{\frac{1}{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}}} {{({{{{\phi_L}} - {{{{\phi_L}}} \cdot {{{ⅇ}^{({{{2}} {{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}})}}}}} + {{{{{{\phi_L}}} \cdot {{{ⅇ}^{({{{2}} {{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}})}}} {{{cos\left( {\theta_L}\right)}^{2}}}} - {{{{\phi_L}}} \cdot {{{cos\left( {\theta_L}\right)}^{2}}}}} - {{\phi_R}}} + {{{{{\phi_R}}} \cdot {{{ⅇ}^{({{{2}} {{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}})}}}} - {{{{\phi_R}}} \cdot {{{ⅇ}^{({{{2}} {{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}})}}} {{{cos\left( {\theta_L}\right)}^{2}}}}} + {{{{\phi_R}}} \cdot {{{cos\left( {\theta_L}\right)}^{2}}}}})}} {{{r_L}}}}{{{2}} {{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}} \\ 0 & \frac{{{cos\left( {\theta_L}\right)}} {{sin\left( {\theta_L}\right)}} {{({{{2} - {{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}} - {\frac{1}{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}}})}}}{-{{{2}} {{{r_L}}}}} & {\frac{1}{2}}{({{{2} - {{{2}} {{{cos\left( {\theta_L}\right)}^{2}}}}} + {{{\frac{1}{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}}} {{{cos\left( {\theta_L}\right)}^{2}}}} + {{{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}} {{{cos\left( {\theta_L}\right)}^{2}}}}})} & \frac{-{{{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}} {{cos\left( {\theta_L}\right)}} {{sin\left( {\theta_L}\right)}} {{({{{{{\phi_L}} - {{\phi_R}}} - {{{{\phi_L}}} \cdot {{\frac{1}{{ⅇ}^{({{{2}} {{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}})}}}}}} + {{{{\phi_R}}} \cdot {{\frac{1}{{ⅇ}^{({{{2}} {{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}})}}}}}})}}}}{{{2}} {{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}} \\ 0 & \frac{{{\frac{1}{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}}} {{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}} {{({{1} - {{ⅇ}^{({{{2}} {{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}})}}})}}}{{{2}} {{({{{\phi_L}} - {{\phi_R}}})}} {{{r_L}}}} & \frac{{{\frac{1}{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}}} {{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}} {{cos\left( {\theta_L}\right)}} {{({{1} - {{ⅇ}^{({{{2}} {{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}})}}})}}}{{{2}} {{sin\left( {\theta_L}\right)}} {{({{{\phi_L}} - {{\phi_R}}})}}} & {\frac{1}{2}}{({{{\frac{1}{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}}} {{({{1} + {{ⅇ}^{({{{2}} {{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}})}}})}}})}\end{matrix}\right]}} - { {\left[\begin{matrix} 1 & 0 & 0 & 0 \\ 0 & \frac{{{{{2}} {{{\phi_L}}} \cdot {{{cos\left( {\theta_R}\right)}^{2}}}} - {{{2}} {{{\phi_R}}} \cdot {{{cos\left( {\theta_R}\right)}^{2}}}}} + {{{{{{\phi_L}}} \cdot {{\frac{1}{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}}}} - {{{{\phi_L}}} \cdot {{\frac{1}{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}}} {{{cos\left( {\theta_R}\right)}^{2}}}}} - {{{{\phi_R}}} \cdot {{\frac{1}{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}}}}} + {{{{\phi_R}}} \cdot {{\frac{1}{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}}} {{{cos\left( {\theta_R}\right)}^{2}}}} + {{{{{{\phi_L}}} \cdot {{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}}} - {{{{\phi_L}}} \cdot {{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}} {{{cos\left( {\theta_R}\right)}^{2}}}}} - {{{{\phi_R}}} \cdot {{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}}}} + {{{{\phi_R}}} \cdot {{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}} {{{cos\left( {\theta_R}\right)}^{2}}}}}{{{2}} {{({{{\phi_L}} - {{\phi_R}}})}}} & \frac{-{{{sin\left( {\theta_R}\right)}} {{cos\left( {\theta_R}\right)}} {{({{{{{{{2}} {{{\phi_L}}}} - {{{{\phi_L}}} \cdot {{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}}}} - {{{{\phi_L}}} \cdot {{\frac{1}{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}}}}} - {{{2}} {{{\phi_R}}}}} + {{{{\phi_R}}} \cdot {{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}}} + {{{{\phi_R}}} \cdot {{\frac{1}{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}}}}})}} {{{r_L}}}}}{{{2}} {{({{{\phi_L}} - {{\phi_R}}})}}} & \frac{{{\frac{1}{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}}} {{({{{{\phi_L}} - {{{{\phi_L}}} \cdot {{{ⅇ}^{({{{2}} {{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}})}}}}} + {{{{{{\phi_L}}} \cdot {{{ⅇ}^{({{{2}} {{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}})}}} {{{cos\left( {\theta_R}\right)}^{2}}}} - {{{{\phi_L}}} \cdot {{{cos\left( {\theta_R}\right)}^{2}}}}} - {{\phi_R}}} + {{{{{\phi_R}}} \cdot {{{ⅇ}^{({{{2}} {{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}})}}}} - {{{{\phi_R}}} \cdot {{{ⅇ}^{({{{2}} {{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}})}}} {{{cos\left( {\theta_R}\right)}^{2}}}}} + {{{{\phi_R}}} \cdot {{{cos\left( {\theta_R}\right)}^{2}}}}})}} {{{r_L}}}}{{{2}} {{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}} \\ 0 & \frac{{{cos\left( {\theta_R}\right)}} {{sin\left( {\theta_R}\right)}} {{({{{2} - {{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}} - {\frac{1}{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}}})}}}{-{{{2}} {{{r_L}}}}} & {\frac{1}{2}}{({{{2} - {{{2}} {{{cos\left( {\theta_R}\right)}^{2}}}}} + {{{\frac{1}{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}}} {{{cos\left( {\theta_R}\right)}^{2}}}} + {{{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}} {{{cos\left( {\theta_R}\right)}^{2}}}}})} & \frac{-{{{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}} {{cos\left( {\theta_R}\right)}} {{sin\left( {\theta_R}\right)}} {{({{{{{\phi_L}} - {{\phi_R}}} - {{{{\phi_L}}} \cdot {{\frac{1}{{ⅇ}^{({{{2}} {{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}})}}}}}} + {{{{\phi_R}}} \cdot {{\frac{1}{{ⅇ}^{({{{2}} {{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}})}}}}}})}}}}{{{2}} {{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}} \\ 0 & \frac{{{\frac{1}{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}}} {{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}} {{({{1} - {{ⅇ}^{({{{2}} {{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}})}}})}}}{{{2}} {{({{{\phi_L}} - {{\phi_R}}})}} {{{r_L}}}} & \frac{{{\frac{1}{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}}} {{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}} {{cos\left( {\theta_R}\right)}} {{({{1} - {{ⅇ}^{({{{2}} {{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}})}}})}}}{{{2}} {{sin\left( {\theta_R}\right)}} {{({{{\phi_L}} - {{\phi_R}}})}}} & {\frac{1}{2}}{({{{\frac{1}{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}}} {{({{1} + {{ⅇ}^{({{{2}} {{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}})}}})}}})}\end{matrix}\right]} {\left[\begin{matrix} 1 & 0 & 0 & 0 \\ 0 & cos\left( {{{\theta_L}} - {{\theta_R}}}\right) & -{{{sin\left( {{{\theta_L}} - {{\theta_R}}}\right)}} {{{r_L}}}} & 0 \\ 0 & {\frac{1}{{r_L}}}{({sin\left( {{{\theta_L}} - {{\theta_R}}}\right)})} & cos\left( {{{\theta_L}} - {{\theta_R}}}\right) & 0 \\ 0 & 0 & 0 & \frac{|{sin\left( {\theta_L}\right)}|}{|{sin\left( {\theta_R}\right)}|}\end{matrix}\right]}}$ = $\left[\begin{matrix} 0 & 0 & 0 & 0 \\ 0 & \frac{-{({{{{{\phi_L}}} \cdot {{{cos\left( {\theta_L}\right)}^{2}}} {{cos\left( {{{\theta_L}} - {{\theta_R}}}\right)}}} + {{{{{\phi_L}}} \cdot {{sin\left( {{{\theta_L}} - {{\theta_R}}}\right)}} {{sin\left( {\theta_L}\right)}} {{cos\left( {\theta_L}\right)}}} - {{{{\phi_L}}} \cdot {{{cos\left( {\theta_R}\right)}^{2}}} {{cos\left( {{{\theta_L}} - {{\theta_R}}}\right)}}}} + {{{{\phi_L}}} \cdot {{sin\left( {{{\theta_L}} - {{\theta_R}}}\right)}} {{sin\left( {\theta_R}\right)}} {{cos\left( {\theta_R}\right)}}} + {{{{{{{\phi_L}}} \cdot {{{ⅇ}^{({{{2}} {{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}})}}} {{{cos\left( {\theta_L}\right)}^{2}}} {{cos\left( {{{\theta_L}} - {{\theta_R}}}\right)}}} - {{{2}} {{{\phi_L}}} \cdot {{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}} {{{cos\left( {\theta_L}\right)}^{2}}} {{cos\left( {{{\theta_L}} - {{\theta_R}}}\right)}}}} - {{{2}} {{{\phi_L}}} \cdot {{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}} {{sin\left( {\theta_L}\right)}} {{cos\left( {\theta_L}\right)}} {{sin\left( {{{\theta_L}} - {{\theta_R}}}\right)}}}} - {{{{\phi_L}}} \cdot {{{ⅇ}^{({{{2}} {{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}})}}} {{{cos\left( {\theta_R}\right)}^{2}}} {{cos\left( {{{\theta_L}} - {{\theta_R}}}\right)}}}} + {{{{2}} {{{\phi_L}}} \cdot {{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}} {{{cos\left( {\theta_R}\right)}^{2}}} {{cos\left( {{{\theta_L}} - {{\theta_R}}}\right)}}} - {{{2}} {{{\phi_L}}} \cdot {{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}} {{sin\left( {\theta_R}\right)}} {{cos\left( {\theta_R}\right)}} {{sin\left( {{{\theta_L}} - {{\theta_R}}}\right)}}}} + {{{{\phi_L}}} \cdot {{{ⅇ}^{({{{2}} {{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}})}}} {{sin\left( {{{\theta_L}} - {{\theta_R}}}\right)}} {{cos\left( {\theta_L}\right)}} {{sin\left( {\theta_L}\right)}}} + {{{{{{\phi_L}}} \cdot {{{ⅇ}^{({{{2}} {{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}})}}} {{sin\left( {{{\theta_L}} - {{\theta_R}}}\right)}} {{cos\left( {\theta_R}\right)}} {{sin\left( {\theta_R}\right)}}} - {{{{\phi_R}}} \cdot {{{cos\left( {\theta_L}\right)}^{2}}} {{cos\left( {{{\theta_L}} - {{\theta_R}}}\right)}}}} - {{{{\phi_R}}} \cdot {{cos\left( {\theta_L}\right)}} {{sin\left( {{{\theta_L}} - {{\theta_R}}}\right)}} {{sin\left( {\theta_L}\right)}}}} + {{{{{{\phi_R}}} \cdot {{{cos\left( {\theta_R}\right)}^{2}}} {{cos\left( {{{\theta_L}} - {{\theta_R}}}\right)}}} - {{{{\phi_R}}} \cdot {{cos\left( {\theta_R}\right)}} {{sin\left( {{{\theta_L}} - {{\theta_R}}}\right)}} {{sin\left( {\theta_R}\right)}}}} - {{{{\phi_R}}} \cdot {{{ⅇ}^{({{{2}} {{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}})}}} {{{cos\left( {\theta_L}\right)}^{2}}} {{cos\left( {{{\theta_L}} - {{\theta_R}}}\right)}}}} + {{{{2}} {{{\phi_R}}} \cdot {{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}} {{{cos\left( {\theta_L}\right)}^{2}}} {{cos\left( {{{\theta_L}} - {{\theta_R}}}\right)}}} - {{{{\phi_R}}} \cdot {{{ⅇ}^{({{{2}} {{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}})}}} {{sin\left( {\theta_L}\right)}} {{cos\left( {\theta_L}\right)}} {{sin\left( {{{\theta_L}} - {{\theta_R}}}\right)}}}} + {{{2}} {{{\phi_R}}} \cdot {{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}} {{sin\left( {\theta_L}\right)}} {{cos\left( {\theta_L}\right)}} {{sin\left( {{{\theta_L}} - {{\theta_R}}}\right)}}} + {{{{{{\phi_R}}} \cdot {{{ⅇ}^{({{{2}} {{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}})}}} {{{cos\left( {\theta_R}\right)}^{2}}} {{cos\left( {{{\theta_L}} - {{\theta_R}}}\right)}}} - {{{2}} {{{\phi_R}}} \cdot {{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}} {{{cos\left( {\theta_R}\right)}^{2}}} {{cos\left( {{{\theta_L}} - {{\theta_R}}}\right)}}}} - {{{{\phi_R}}} \cdot {{{ⅇ}^{({{{2}} {{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}})}}} {{sin\left( {\theta_R}\right)}} {{cos\left( {\theta_R}\right)}} {{sin\left( {{{\theta_L}} - {{\theta_R}}}\right)}}}} + {{{2}} {{{\phi_R}}} \cdot {{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}} {{sin\left( {\theta_R}\right)}} {{cos\left( {\theta_R}\right)}} {{sin\left( {{{\theta_L}} - {{\theta_R}}}\right)}}}})}}{{{2}} {{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}} {{({{{\phi_L}} - {{\phi_R}}})}}} & \frac{-{{{{r_L}}} \cdot {{({{{{{{\phi_L}}} \cdot {{{cos\left( {\theta_L}\right)}^{2}}} {{sin\left( {{{\theta_L}} - {{\theta_R}}}\right)}}} - {{{{\phi_L}}} \cdot {{cos\left( {\theta_L}\right)}} {{cos\left( {{{\theta_L}} - {{\theta_R}}}\right)}} {{sin\left( {\theta_L}\right)}}}} + {{{{\phi_L}}} \cdot {{{cos\left( {\theta_R}\right)}^{2}}} {{sin\left( {{{\theta_L}} - {{\theta_R}}}\right)}}} + {{{{{{{\phi_L}}} \cdot {{cos\left( {{{\theta_L}} - {{\theta_R}}}\right)}} {{sin\left( {\theta_R}\right)}} {{cos\left( {\theta_R}\right)}}} - {{{{\phi_L}}} \cdot {{sin\left( {{{\theta_L}} - {{\theta_R}}}\right)}}}} - {{{{\phi_L}}} \cdot {{{ⅇ}^{({{{2}} {{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}})}}} {{sin\left( {\theta_L}\right)}} {{cos\left( {\theta_L}\right)}} {{cos\left( {{{\theta_L}} - {{\theta_R}}}\right)}}}} - {{{2}} {{{\phi_L}}} \cdot {{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}} {{{cos\left( {\theta_L}\right)}^{2}}} {{sin\left( {{{\theta_L}} - {{\theta_R}}}\right)}}}} + {{{{\phi_L}}} \cdot {{{ⅇ}^{({{{2}} {{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}})}}} {{{cos\left( {\theta_L}\right)}^{2}}} {{sin\left( {{{\theta_L}} - {{\theta_R}}}\right)}}} + {{{2}} {{{\phi_L}}} \cdot {{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}} {{sin\left( {\theta_L}\right)}} {{cos\left( {\theta_L}\right)}} {{cos\left( {{{\theta_L}} - {{\theta_R}}}\right)}}} + {{{{{{\phi_L}}} \cdot {{{ⅇ}^{({{{2}} {{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}})}}} {{{cos\left( {\theta_R}\right)}^{2}}} {{sin\left( {{{\theta_L}} - {{\theta_R}}}\right)}}} - {{{2}} {{{\phi_L}}} \cdot {{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}} {{{cos\left( {\theta_R}\right)}^{2}}} {{sin\left( {{{\theta_L}} - {{\theta_R}}}\right)}}}} - {{{2}} {{{\phi_L}}} \cdot {{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}} {{sin\left( {\theta_R}\right)}} {{cos\left( {\theta_R}\right)}} {{cos\left( {{{\theta_L}} - {{\theta_R}}}\right)}}}} + {{{{{\phi_L}}} \cdot {{{ⅇ}^{({{{2}} {{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}})}}} {{cos\left( {{{\theta_L}} - {{\theta_R}}}\right)}} {{cos\left( {\theta_R}\right)}} {{sin\left( {\theta_R}\right)}}} - {{{{\phi_L}}} \cdot {{{ⅇ}^{({{{2}} {{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}})}}} {{sin\left( {{{\theta_L}} - {{\theta_R}}}\right)}}}} + {{{{2}} {{{\phi_L}}} \cdot {{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}} {{sin\left( {{{\theta_L}} - {{\theta_R}}}\right)}}} - {{{{\phi_R}}} \cdot {{{cos\left( {\theta_L}\right)}^{2}}} {{sin\left( {{{\theta_L}} - {{\theta_R}}}\right)}}}} + {{{{{{\phi_R}}} \cdot {{cos\left( {{{\theta_L}} - {{\theta_R}}}\right)}} {{sin\left( {\theta_L}\right)}} {{cos\left( {\theta_L}\right)}}} - {{{{\phi_R}}} \cdot {{{cos\left( {\theta_R}\right)}^{2}}} {{sin\left( {{{\theta_L}} - {{\theta_R}}}\right)}}}} - {{{{\phi_R}}} \cdot {{cos\left( {\theta_R}\right)}} {{cos\left( {{{\theta_L}} - {{\theta_R}}}\right)}} {{sin\left( {\theta_R}\right)}}}} + {{{{{{\phi_R}}} \cdot {{sin\left( {{{\theta_L}} - {{\theta_R}}}\right)}}} - {{{{\phi_R}}} \cdot {{{ⅇ}^{({{{2}} {{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}})}}} {{sin\left( {\theta_R}\right)}} {{cos\left( {\theta_R}\right)}} {{cos\left( {{{\theta_L}} - {{\theta_R}}}\right)}}}} - {{{{\phi_R}}} \cdot {{{ⅇ}^{({{{2}} {{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}})}}} {{{cos\left( {\theta_L}\right)}^{2}}} {{sin\left( {{{\theta_L}} - {{\theta_R}}}\right)}}}} + {{{{2}} {{{\phi_R}}} \cdot {{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}} {{{cos\left( {\theta_L}\right)}^{2}}} {{sin\left( {{{\theta_L}} - {{\theta_R}}}\right)}}} - {{{2}} {{{\phi_R}}} \cdot {{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}} {{sin\left( {\theta_L}\right)}} {{cos\left( {\theta_L}\right)}} {{cos\left( {{{\theta_L}} - {{\theta_R}}}\right)}}}} + {{{{\phi_R}}} \cdot {{{ⅇ}^{({{{2}} {{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}})}}} {{cos\left( {{{\theta_L}} - {{\theta_R}}}\right)}} {{cos\left( {\theta_L}\right)}} {{sin\left( {\theta_L}\right)}}} + {{{{2}} {{{\phi_R}}} \cdot {{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}} {{{cos\left( {\theta_R}\right)}^{2}}} {{sin\left( {{{\theta_L}} - {{\theta_R}}}\right)}}} - {{{{\phi_R}}} \cdot {{{ⅇ}^{({{{2}} {{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}})}}} {{{cos\left( {\theta_R}\right)}^{2}}} {{sin\left( {{{\theta_L}} - {{\theta_R}}}\right)}}}} + {{{2}} {{{\phi_R}}} \cdot {{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}} {{sin\left( {\theta_R}\right)}} {{cos\left( {\theta_R}\right)}} {{cos\left( {{{\theta_L}} - {{\theta_R}}}\right)}}} + {{{{{\phi_R}}} \cdot {{{ⅇ}^{({{{2}} {{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}})}}} {{sin\left( {{{\theta_L}} - {{\theta_R}}}\right)}}} - {{{2}} {{{\phi_R}}} \cdot {{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}} {{sin\left( {{{\theta_L}} - {{\theta_R}}}\right)}}}}})}}}}{{{2}} {{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}} {{({{{\phi_L}} - {{\phi_R}}})}}} & \frac{-{{{{r_L}}} \cdot {{({{{{{{\phi_L}}} \cdot {{|{sin\left( {\theta_L}\right)}|}}} - {{{{\phi_L}}} \cdot {{cos\left( {{{\theta_L}} - {{\theta_R}}}\right)}} {{|{sin\left( {\theta_R}\right)}|}}}} + {{{{\phi_L}}} \cdot {{{cos\left( {\theta_L}\right)}^{2}}} {{cos\left( {{{\theta_L}} - {{\theta_R}}}\right)}} {{|{sin\left( {\theta_R}\right)}|}}} + {{{{{{\phi_L}}} \cdot {{sin\left( {\theta_L}\right)}} {{sin\left( {{{\theta_L}} - {{\theta_R}}}\right)}} {{cos\left( {\theta_L}\right)}} {{|{sin\left( {\theta_R}\right)}|}}} - {{{{\phi_L}}} \cdot {{{cos\left( {\theta_R}\right)}^{2}}} {{|{sin\left( {\theta_L}\right)}|}}}} - {{{{\phi_L}}} \cdot {{{ⅇ}^{({{{2}} {{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}})}}} {{|{sin\left( {\theta_L}\right)}|}}}} + {{{{{\phi_L}}} \cdot {{{ⅇ}^{({{{2}} {{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}})}}} {{cos\left( {{{\theta_L}} - {{\theta_R}}}\right)}} {{|{sin\left( {\theta_R}\right)}|}}} - {{{{\phi_L}}} \cdot {{{ⅇ}^{({{{2}} {{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}})}}} {{{cos\left( {\theta_L}\right)}^{2}}} {{cos\left( {{{\theta_L}} - {{\theta_R}}}\right)}} {{|{sin\left( {\theta_R}\right)}|}}}} + {{{{{{\phi_L}}} \cdot {{{ⅇ}^{({{{2}} {{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}})}}} {{{cos\left( {\theta_R}\right)}^{2}}} {{|{sin\left( {\theta_L}\right)}|}}} - {{{{\phi_L}}} \cdot {{{ⅇ}^{({{{2}} {{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}})}}} {{sin\left( {{{\theta_L}} - {{\theta_R}}}\right)}} {{|{sin\left( {\theta_R}\right)}|}} {{sin\left( {\theta_L}\right)}} {{cos\left( {\theta_L}\right)}}}} - {{{{\phi_R}}} \cdot {{|{sin\left( {\theta_L}\right)}|}}}} + {{{{{{\phi_R}}} \cdot {{|{sin\left( {\theta_R}\right)}|}} {{cos\left( {{{\theta_L}} - {{\theta_R}}}\right)}}} - {{{{\phi_R}}} \cdot {{{cos\left( {\theta_L}\right)}^{2}}} {{|{sin\left( {\theta_R}\right)}|}} {{cos\left( {{{\theta_L}} - {{\theta_R}}}\right)}}}} - {{{{\phi_R}}} \cdot {{cos\left( {\theta_L}\right)}} {{sin\left( {\theta_L}\right)}} {{|{sin\left( {\theta_R}\right)}|}} {{sin\left( {{{\theta_L}} - {{\theta_R}}}\right)}}}} + {{{{\phi_R}}} \cdot {{{cos\left( {\theta_R}\right)}^{2}}} {{|{sin\left( {\theta_L}\right)}|}}} + {{{{{\phi_R}}} \cdot {{{ⅇ}^{({{{2}} {{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}})}}} {{|{sin\left( {\theta_L}\right)}|}}} - {{{{\phi_R}}} \cdot {{{ⅇ}^{({{{2}} {{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}})}}} {{|{sin\left( {\theta_R}\right)}|}} {{cos\left( {{{\theta_L}} - {{\theta_R}}}\right)}}}} + {{{{{\phi_R}}} \cdot {{{ⅇ}^{({{{2}} {{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}})}}} {{{cos\left( {\theta_L}\right)}^{2}}} {{|{sin\left( {\theta_R}\right)}|}} {{cos\left( {{{\theta_L}} - {{\theta_R}}}\right)}}} - {{{{\phi_R}}} \cdot {{{ⅇ}^{({{{2}} {{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}})}}} {{{cos\left( {\theta_R}\right)}^{2}}} {{|{sin\left( {\theta_L}\right)}|}}}} + {{{{\phi_R}}} \cdot {{{ⅇ}^{({{{2}} {{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}})}}} {{cos\left( {\theta_L}\right)}} {{sin\left( {\theta_L}\right)}} {{sin\left( {{{\theta_L}} - {{\theta_R}}}\right)}} {{|{sin\left( {\theta_R}\right)}|}}}})}}}}{{{2}} {{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}} {{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}} {{|{sin\left( {\theta_R}\right)}|}}} \\ 0 & \frac{{-{{{{\phi_L}}} \cdot {{{cos\left( {\theta_L}\right)}^{2}}} {{sin\left( {{{\theta_L}} - {{\theta_R}}}\right)}}}} + {{{{\phi_L}}} \cdot {{cos\left( {\theta_L}\right)}} {{sin\left( {\theta_L}\right)}} {{cos\left( {{{\theta_L}} - {{\theta_R}}}\right)}}} + {{{{{{{\phi_L}}} \cdot {{sin\left( {{{\theta_L}} - {{\theta_R}}}\right)}}} - {{{{\phi_L}}} \cdot {{{cos\left( {\theta_R}\right)}^{2}}} {{sin\left( {{{\theta_L}} - {{\theta_R}}}\right)}}}} - {{{{\phi_L}}} \cdot {{cos\left( {\theta_R}\right)}} {{sin\left( {\theta_R}\right)}} {{cos\left( {{{\theta_L}} - {{\theta_R}}}\right)}}}} - {{{{\phi_L}}} \cdot {{{ⅇ}^{({{{2}} {{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}})}}} {{cos\left( {{{\theta_L}} - {{\theta_R}}}\right)}} {{sin\left( {\theta_R}\right)}} {{cos\left( {\theta_R}\right)}}}} + {{{{{2}} {{{\phi_L}}} \cdot {{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}} {{{cos\left( {\theta_L}\right)}^{2}}} {{sin\left( {{{\theta_L}} - {{\theta_R}}}\right)}}} - {{{{\phi_L}}} \cdot {{{ⅇ}^{({{{2}} {{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}})}}} {{{cos\left( {\theta_L}\right)}^{2}}} {{sin\left( {{{\theta_L}} - {{\theta_R}}}\right)}}}} - {{{2}} {{{\phi_L}}} \cdot {{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}} {{cos\left( {\theta_L}\right)}} {{sin\left( {\theta_L}\right)}} {{cos\left( {{{\theta_L}} - {{\theta_R}}}\right)}}}} + {{{{\phi_L}}} \cdot {{{ⅇ}^{({{{2}} {{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}})}}} {{cos\left( {\theta_L}\right)}} {{sin\left( {\theta_L}\right)}} {{cos\left( {{{\theta_L}} - {{\theta_R}}}\right)}}} + {{{{{{\phi_L}}} \cdot {{{ⅇ}^{({{{2}} {{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}})}}} {{sin\left( {{{\theta_L}} - {{\theta_R}}}\right)}}} - {{{{\phi_L}}} \cdot {{{ⅇ}^{({{{2}} {{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}})}}} {{{cos\left( {\theta_R}\right)}^{2}}} {{sin\left( {{{\theta_L}} - {{\theta_R}}}\right)}}}} - {{{2}} {{{\phi_L}}} \cdot {{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}} {{sin\left( {{{\theta_L}} - {{\theta_R}}}\right)}}}} + {{{2}} {{{\phi_L}}} \cdot {{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}} {{{cos\left( {\theta_R}\right)}^{2}}} {{sin\left( {{{\theta_L}} - {{\theta_R}}}\right)}}} + {{{2}} {{{\phi_L}}} \cdot {{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}} {{cos\left( {\theta_R}\right)}} {{sin\left( {\theta_R}\right)}} {{cos\left( {{{\theta_L}} - {{\theta_R}}}\right)}}} + {{{{{{\phi_R}}} \cdot {{{cos\left( {\theta_L}\right)}^{2}}} {{sin\left( {{{\theta_L}} - {{\theta_R}}}\right)}}} - {{{{\phi_R}}} \cdot {{cos\left( {\theta_L}\right)}} {{sin\left( {\theta_L}\right)}} {{cos\left( {{{\theta_L}} - {{\theta_R}}}\right)}}}} - {{{{\phi_R}}} \cdot {{sin\left( {{{\theta_L}} - {{\theta_R}}}\right)}}}} + {{{{\phi_R}}} \cdot {{{cos\left( {\theta_R}\right)}^{2}}} {{sin\left( {{{\theta_L}} - {{\theta_R}}}\right)}}} + {{{{{{\phi_R}}} \cdot {{cos\left( {\theta_R}\right)}} {{sin\left( {\theta_R}\right)}} {{cos\left( {{{\theta_L}} - {{\theta_R}}}\right)}}} - {{{{\phi_R}}} \cdot {{{ⅇ}^{({{{2}} {{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}})}}} {{cos\left( {{{\theta_L}} - {{\theta_R}}}\right)}} {{sin\left( {\theta_L}\right)}} {{cos\left( {\theta_L}\right)}}}} - {{{2}} {{{\phi_R}}} \cdot {{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}} {{{cos\left( {\theta_L}\right)}^{2}}} {{sin\left( {{{\theta_L}} - {{\theta_R}}}\right)}}}} + {{{{\phi_R}}} \cdot {{{ⅇ}^{({{{2}} {{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}})}}} {{{cos\left( {\theta_L}\right)}^{2}}} {{sin\left( {{{\theta_L}} - {{\theta_R}}}\right)}}} + {{{2}} {{{\phi_R}}} \cdot {{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}} {{cos\left( {\theta_L}\right)}} {{sin\left( {\theta_L}\right)}} {{cos\left( {{{\theta_L}} - {{\theta_R}}}\right)}}} + {{{{{2}} {{{\phi_R}}} \cdot {{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}} {{sin\left( {{{\theta_L}} - {{\theta_R}}}\right)}}} - {{{2}} {{{\phi_R}}} \cdot {{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}} {{{cos\left( {\theta_R}\right)}^{2}}} {{sin\left( {{{\theta_L}} - {{\theta_R}}}\right)}}}} - {{{{\phi_R}}} \cdot {{{ⅇ}^{({{{2}} {{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}})}}} {{sin\left( {{{\theta_L}} - {{\theta_R}}}\right)}}}} + {{{{{\phi_R}}} \cdot {{{ⅇ}^{({{{2}} {{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}})}}} {{{cos\left( {\theta_R}\right)}^{2}}} {{sin\left( {{{\theta_L}} - {{\theta_R}}}\right)}}} - {{{2}} {{{\phi_R}}} \cdot {{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}} {{cos\left( {\theta_R}\right)}} {{sin\left( {\theta_R}\right)}} {{cos\left( {{{\theta_L}} - {{\theta_R}}}\right)}}}} + {{{{\phi_R}}} \cdot {{{ⅇ}^{({{{2}} {{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}})}}} {{cos\left( {\theta_R}\right)}} {{sin\left( {\theta_R}\right)}} {{cos\left( {{{\theta_L}} - {{\theta_R}}}\right)}}}}{{{2}} {{{r_L}}} \cdot {{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}} {{({{{\phi_L}} - {{\phi_R}}})}}} & \frac{{{{{{2}} {{{\phi_L}}} \cdot {{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}} {{{cos\left( {\theta_R}\right)}^{2}}} {{cos\left( {{{\theta_L}} - {{\theta_R}}}\right)}}} - {{{2}} {{{\phi_R}}} \cdot {{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}} {{{cos\left( {\theta_R}\right)}^{2}}} {{cos\left( {{{\theta_L}} - {{\theta_R}}}\right)}}}} - {{{{\phi_L}}} \cdot {{{ⅇ}^{({{{2}} {{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}})}}} {{{cos\left( {\theta_R}\right)}^{2}}} {{cos\left( {{{\theta_L}} - {{\theta_R}}}\right)}}}} + {{{{{\phi_R}}} \cdot {{{ⅇ}^{({{{2}} {{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}})}}} {{{cos\left( {\theta_R}\right)}^{2}}} {{cos\left( {{{\theta_L}} - {{\theta_R}}}\right)}}} - {{{{\phi_L}}} \cdot {{{cos\left( {\theta_R}\right)}^{2}}} {{cos\left( {{{\theta_L}} - {{\theta_R}}}\right)}}}} + {{{{\phi_R}}} \cdot {{{cos\left( {\theta_R}\right)}^{2}}} {{cos\left( {{{\theta_L}} - {{\theta_R}}}\right)}}} + {{{{{{\phi_L}}} \cdot {{sin\left( {{{\theta_L}} - {{\theta_R}}}\right)}} {{cos\left( {\theta_R}\right)}} {{sin\left( {\theta_R}\right)}}} - {{{{\phi_R}}} \cdot {{sin\left( {\theta_R}\right)}} {{cos\left( {\theta_R}\right)}} {{sin\left( {{{\theta_L}} - {{\theta_R}}}\right)}}}} - {{{2}} {{{\phi_L}}} \cdot {{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}} {{cos\left( {\theta_R}\right)}} {{sin\left( {\theta_R}\right)}} {{sin\left( {{{\theta_L}} - {{\theta_R}}}\right)}}}} + {{{2}} {{{\phi_R}}} \cdot {{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}} {{cos\left( {\theta_R}\right)}} {{sin\left( {{{\theta_L}} - {{\theta_R}}}\right)}} {{sin\left( {\theta_R}\right)}}} + {{{{{{\phi_L}}} \cdot {{{ⅇ}^{({{{2}} {{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}})}}} {{sin\left( {{{\theta_L}} - {{\theta_R}}}\right)}} {{sin\left( {\theta_R}\right)}} {{cos\left( {\theta_R}\right)}}} - {{{{\phi_R}}} \cdot {{{ⅇ}^{({{{2}} {{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}})}}} {{cos\left( {\theta_R}\right)}} {{sin\left( {{{\theta_L}} - {{\theta_R}}}\right)}} {{sin\left( {\theta_R}\right)}}}} - {{{2}} {{{\phi_L}}} \cdot {{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}} {{{cos\left( {\theta_L}\right)}^{2}}} {{cos\left( {{{\theta_L}} - {{\theta_R}}}\right)}}}} + {{{2}} {{{\phi_R}}} \cdot {{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}} {{{cos\left( {\theta_L}\right)}^{2}}} {{cos\left( {{{\theta_L}} - {{\theta_R}}}\right)}}} + {{{{{\phi_L}}} \cdot {{{ⅇ}^{({{{2}} {{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}})}}} {{{cos\left( {\theta_L}\right)}^{2}}} {{cos\left( {{{\theta_L}} - {{\theta_R}}}\right)}}} - {{{{\phi_R}}} \cdot {{{ⅇ}^{({{{2}} {{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}})}}} {{{cos\left( {\theta_L}\right)}^{2}}} {{cos\left( {{{\theta_L}} - {{\theta_R}}}\right)}}}} + {{{{{{{\phi_L}}} \cdot {{{cos\left( {\theta_L}\right)}^{2}}} {{cos\left( {{{\theta_L}} - {{\theta_R}}}\right)}}} - {{{{\phi_R}}} \cdot {{{cos\left( {\theta_L}\right)}^{2}}} {{cos\left( {{{\theta_L}} - {{\theta_R}}}\right)}}}} - {{{{\phi_R}}} \cdot {{{ⅇ}^{({{{2}} {{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}})}}} {{sin\left( {{{\theta_L}} - {{\theta_R}}}\right)}} {{sin\left( {\theta_L}\right)}} {{cos\left( {\theta_L}\right)}}}} - {{{{\phi_R}}} \cdot {{sin\left( {{{\theta_L}} - {{\theta_R}}}\right)}} {{sin\left( {\theta_L}\right)}} {{cos\left( {\theta_L}\right)}}}} + {{{{2}} {{{\phi_R}}} \cdot {{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}} {{sin\left( {{{\theta_L}} - {{\theta_R}}}\right)}} {{sin\left( {\theta_L}\right)}} {{cos\left( {\theta_L}\right)}}} - {{{2}} {{{\phi_L}}} \cdot {{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}} {{sin\left( {{{\theta_L}} - {{\theta_R}}}\right)}} {{sin\left( {\theta_L}\right)}} {{cos\left( {\theta_L}\right)}}}} + {{{{\phi_L}}} \cdot {{{ⅇ}^{({{{2}} {{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}})}}} {{sin\left( {{{\theta_L}} - {{\theta_R}}}\right)}} {{sin\left( {\theta_L}\right)}} {{cos\left( {\theta_L}\right)}}} + {{{{\phi_L}}} \cdot {{sin\left( {{{\theta_L}} - {{\theta_R}}}\right)}} {{sin\left( {\theta_L}\right)}} {{cos\left( {\theta_L}\right)}}}}{{{2}} {{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}} {{({{{\phi_L}} - {{\phi_R}}})}}} & \frac{{{{{{{\phi_L}}} \cdot {{|{sin\left( {\theta_R}\right)}|}} {{sin\left( {{{\theta_L}} - {{\theta_R}}}\right)}}} - {{{{\phi_L}}} \cdot {{{cos\left( {\theta_L}\right)}^{2}}} {{|{sin\left( {\theta_R}\right)}|}} {{sin\left( {{{\theta_L}} - {{\theta_R}}}\right)}}}} - {{{{\phi_L}}} \cdot {{cos\left( {\theta_R}\right)}} {{sin\left( {\theta_R}\right)}} {{|{sin\left( {\theta_L}\right)}|}}}} + {{{{{{\phi_L}}} \cdot {{|{sin\left( {\theta_R}\right)}|}} {{cos\left( {\theta_L}\right)}} {{sin\left( {\theta_L}\right)}} {{cos\left( {{{\theta_L}} - {{\theta_R}}}\right)}}} - {{{{\phi_L}}} \cdot {{{ⅇ}^{({{{2}} {{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}})}}} {{|{sin\left( {\theta_R}\right)}|}} {{sin\left( {\theta_L}\right)}} {{cos\left( {\theta_L}\right)}} {{cos\left( {{{\theta_L}} - {{\theta_R}}}\right)}}}} - {{{{\phi_L}}} \cdot {{{ⅇ}^{({{{2}} {{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}})}}} {{|{sin\left( {\theta_R}\right)}|}} {{sin\left( {{{\theta_L}} - {{\theta_R}}}\right)}}}} + {{{{\phi_L}}} \cdot {{{ⅇ}^{({{{2}} {{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}})}}} {{{cos\left( {\theta_L}\right)}^{2}}} {{|{sin\left( {\theta_R}\right)}|}} {{sin\left( {{{\theta_L}} - {{\theta_R}}}\right)}}} + {{{{\phi_L}}} \cdot {{{ⅇ}^{({{{2}} {{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}})}}} {{cos\left( {\theta_R}\right)}} {{sin\left( {\theta_R}\right)}} {{|{sin\left( {\theta_L}\right)}|}}} + {{{{{{\phi_R}}} \cdot {{cos\left( {\theta_R}\right)}} {{sin\left( {\theta_R}\right)}} {{|{sin\left( {\theta_L}\right)}|}}} - {{{{\phi_R}}} \cdot {{cos\left( {{{\theta_L}} - {{\theta_R}}}\right)}} {{sin\left( {\theta_L}\right)}} {{cos\left( {\theta_L}\right)}} {{|{sin\left( {\theta_R}\right)}|}}}} - {{{{\phi_R}}} \cdot {{|{sin\left( {\theta_R}\right)}|}} {{sin\left( {{{\theta_L}} - {{\theta_R}}}\right)}}}} + {{{{\phi_R}}} \cdot {{{cos\left( {\theta_L}\right)}^{2}}} {{|{sin\left( {\theta_R}\right)}|}} {{sin\left( {{{\theta_L}} - {{\theta_R}}}\right)}}} + {{{{\phi_R}}} \cdot {{{ⅇ}^{({{{2}} {{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}})}}} {{cos\left( {\theta_L}\right)}} {{sin\left( {\theta_L}\right)}} {{cos\left( {{{\theta_L}} - {{\theta_R}}}\right)}} {{|{sin\left( {\theta_R}\right)}|}}} + {{{{{{\phi_R}}} \cdot {{{ⅇ}^{({{{2}} {{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}})}}} {{|{sin\left( {\theta_R}\right)}|}} {{sin\left( {{{\theta_L}} - {{\theta_R}}}\right)}}} - {{{{\phi_R}}} \cdot {{{ⅇ}^{({{{2}} {{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}})}}} {{{cos\left( {\theta_L}\right)}^{2}}} {{|{sin\left( {\theta_R}\right)}|}} {{sin\left( {{{\theta_L}} - {{\theta_R}}}\right)}}}} - {{{{\phi_R}}} \cdot {{{ⅇ}^{({{{2}} {{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}})}}} {{|{sin\left( {\theta_L}\right)}|}} {{sin\left( {\theta_R}\right)}} {{cos\left( {\theta_R}\right)}}}}}{{{2}} {{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}} {{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}} {{|{sin\left( {\theta_R}\right)}|}}} \\ 0 & \frac{-{{{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}} {{({{{{{|{sin\left( {\theta_R}\right)}|}} {{cos\left( {\theta_R}\right)}} {{sin\left( {{{\theta_L}} - {{\theta_R}}}\right)}}} - {{{sin\left( {\theta_R}\right)}} {{|{sin\left( {\theta_L}\right)}|}}}} + {{{|{sin\left( {\theta_R}\right)}|}} {{sin\left( {\theta_R}\right)}} {{cos\left( {{{\theta_L}} - {{\theta_R}}}\right)}}} + {{{{{{ⅇ}^{({{{2}} {{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}})}}} {{|{sin\left( {\theta_L}\right)}|}} {{sin\left( {\theta_R}\right)}}} - {{{{ⅇ}^{({{{2}} {{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}})}}} {{cos\left( {{{\theta_L}} - {{\theta_R}}}\right)}} {{sin\left( {\theta_R}\right)}} {{|{sin\left( {\theta_R}\right)}|}}}} - {{{{ⅇ}^{({{{2}} {{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}})}}} {{sin\left( {{{\theta_L}} - {{\theta_R}}}\right)}} {{cos\left( {\theta_R}\right)}} {{|{sin\left( {\theta_R}\right)}|}}}}})}}}}{{{2}} {{{r_L}}} \cdot {{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}} {{|{sin\left( {\theta_R}\right)}|}} {{sin\left( {\theta_R}\right)}} {{({{{\phi_L}} - {{\phi_R}}})}}} & \frac{{{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}} {{({{{{sin\left( {\theta_R}\right)}} {{cos\left( {\theta_L}\right)}} {{|{sin\left( {\theta_L}\right)}|}}} + {{{{{sin\left( {\theta_L}\right)}} {{sin\left( {\theta_R}\right)}} {{|{sin\left( {\theta_R}\right)}|}} {{sin\left( {{{\theta_L}} - {{\theta_R}}}\right)}}} - {{{sin\left( {\theta_L}\right)}} {{cos\left( {{{\theta_L}} - {{\theta_R}}}\right)}} {{cos\left( {\theta_R}\right)}} {{|{sin\left( {\theta_R}\right)}|}}}} - {{{{ⅇ}^{({{{2}} {{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}})}}} {{sin\left( {\theta_L}\right)}} {{sin\left( {\theta_R}\right)}} {{sin\left( {{{\theta_L}} - {{\theta_R}}}\right)}} {{|{sin\left( {\theta_R}\right)}|}}}} + {{{{{ⅇ}^{({{{2}} {{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}})}}} {{|{sin\left( {\theta_R}\right)}|}} {{cos\left( {{{\theta_L}} - {{\theta_R}}}\right)}} {{cos\left( {\theta_R}\right)}} {{sin\left( {\theta_L}\right)}}} - {{{{ⅇ}^{({{{2}} {{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}})}}} {{|{sin\left( {\theta_L}\right)}|}} {{cos\left( {\theta_L}\right)}} {{sin\left( {\theta_R}\right)}}}}})}}}{{{2}} {{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}} {{sin\left( {\theta_R}\right)}} {{|{sin\left( {\theta_R}\right)}|}} {{({{{\phi_L}} - {{\phi_R}}})}} {{sin\left( {\theta_L}\right)}}} & 0\end{matrix}\right]$
propagator partials
${{\frac{\partial}{\partial t}}\left( \left[\begin{matrix} 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 1\end{matrix}\right]\right)} = {\left[\begin{matrix} 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0\end{matrix}\right]}$
${{\frac{\partial}{\partial r}}\left( \left[\begin{matrix} 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 1\end{matrix}\right]\right)} = {\left[\begin{matrix} 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0\end{matrix}\right]}$
${{\frac{\partial}{\partial \theta}}\left( \left[\begin{matrix} 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 1\end{matrix}\right]\right)} = {\left[\begin{matrix} 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0\end{matrix}\right]}$
${{\frac{\partial}{\partial \phi}}\left( \left[\begin{matrix} 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 1\end{matrix}\right]\right)} = {\left[\begin{matrix} 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0\end{matrix}\right]}$
${{\frac{\partial}{\partial t}}\left( \left[\begin{matrix} 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & {\frac{1}{{r_R}}}{({{r_L}})} & 0 \\ 0 & 0 & 0 & {\frac{1}{{r_R}}}{({{r_L}})}\end{matrix}\right]\right)} = {\left[\begin{matrix} 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0\end{matrix}\right]}$
${{\frac{\partial}{\partial r}}\left( \left[\begin{matrix} 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & {\frac{1}{{r_R}}}{({{r_L}})} & 0 \\ 0 & 0 & 0 & {\frac{1}{{r_R}}}{({{r_L}})}\end{matrix}\right]\right)} = {\left[\begin{matrix} 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0\end{matrix}\right]}$
${{\frac{\partial}{\partial \theta}}\left( \left[\begin{matrix} 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & {\frac{1}{{r_R}}}{({{r_L}})} & 0 \\ 0 & 0 & 0 & {\frac{1}{{r_R}}}{({{r_L}})}\end{matrix}\right]\right)} = {\left[\begin{matrix} 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0\end{matrix}\right]}$
${{\frac{\partial}{\partial \phi}}\left( \left[\begin{matrix} 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & {\frac{1}{{r_R}}}{({{r_L}})} & 0 \\ 0 & 0 & 0 & {\frac{1}{{r_R}}}{({{r_L}})}\end{matrix}\right]\right)} = {\left[\begin{matrix} 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0\end{matrix}\right]}$
${{\frac{\partial}{\partial t}}\left( \left[\begin{matrix} 1 & 0 & 0 & 0 \\ 0 & cos\left( {{{\theta_L}} - {{\theta_R}}}\right) & -{{{r}} {{sin\left( {{{\theta_L}} - {{\theta_R}}}\right)}}} & 0 \\ 0 & {\frac{1}{r}}{({sin\left( {{{\theta_L}} - {{\theta_R}}}\right)})} & cos\left( {{{\theta_L}} - {{\theta_R}}}\right) & 0 \\ 0 & 0 & 0 & \frac{|{sin\left( {\theta_L}\right)}|}{|{sin\left( {\theta_R}\right)}|}\end{matrix}\right]\right)} = {\left[\begin{matrix} 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0\end{matrix}\right]}$
${{\frac{\partial}{\partial r}}\left( \left[\begin{matrix} 1 & 0 & 0 & 0 \\ 0 & cos\left( {{{\theta_L}} - {{\theta_R}}}\right) & -{{{r}} {{sin\left( {{{\theta_L}} - {{\theta_R}}}\right)}}} & 0 \\ 0 & {\frac{1}{r}}{({sin\left( {{{\theta_L}} - {{\theta_R}}}\right)})} & cos\left( {{{\theta_L}} - {{\theta_R}}}\right) & 0 \\ 0 & 0 & 0 & \frac{|{sin\left( {\theta_L}\right)}|}{|{sin\left( {\theta_R}\right)}|}\end{matrix}\right]\right)} = {\left[\begin{matrix} 0 & 0 & 0 & 0 \\ 0 & 0 & -{sin\left( {{{\theta_L}} - {{\theta_R}}}\right)} & 0 \\ 0 & \frac{-{sin\left( {{{\theta_L}} - {{\theta_R}}}\right)}}{{r}^{2}} & 0 & 0 \\ 0 & 0 & 0 & 0\end{matrix}\right]}$
${{\frac{\partial}{\partial \theta}}\left( \left[\begin{matrix} 1 & 0 & 0 & 0 \\ 0 & cos\left( {{{\theta_L}} - {{\theta_R}}}\right) & -{{{r}} {{sin\left( {{{\theta_L}} - {{\theta_R}}}\right)}}} & 0 \\ 0 & {\frac{1}{r}}{({sin\left( {{{\theta_L}} - {{\theta_R}}}\right)})} & cos\left( {{{\theta_L}} - {{\theta_R}}}\right) & 0 \\ 0 & 0 & 0 & \frac{|{sin\left( {\theta_L}\right)}|}{|{sin\left( {\theta_R}\right)}|}\end{matrix}\right]\right)} = {\left[\begin{matrix} 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0\end{matrix}\right]}$
${{\frac{\partial}{\partial \phi}}\left( \left[\begin{matrix} 1 & 0 & 0 & 0 \\ 0 & cos\left( {{{\theta_L}} - {{\theta_R}}}\right) & -{{{r}} {{sin\left( {{{\theta_L}} - {{\theta_R}}}\right)}}} & 0 \\ 0 & {\frac{1}{r}}{({sin\left( {{{\theta_L}} - {{\theta_R}}}\right)})} & cos\left( {{{\theta_L}} - {{\theta_R}}}\right) & 0 \\ 0 & 0 & 0 & \frac{|{sin\left( {\theta_L}\right)}|}{|{sin\left( {\theta_R}\right)}|}\end{matrix}\right]\right)} = {\left[\begin{matrix} 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0\end{matrix}\right]}$
${{\frac{\partial}{\partial t}}\left( \left[\begin{matrix} 1 & 0 & 0 & 0 \\ 0 & \frac{{{{{2}} {{{\phi_L}}} \cdot {{{cos\left( \theta\right)}^{2}}}} - {{{2}} {{{\phi_R}}} \cdot {{{cos\left( \theta\right)}^{2}}}}} + {{{{{{\phi_L}}} \cdot {{\frac{1}{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}}}} - {{{{\phi_L}}} \cdot {{\frac{1}{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}}} {{{cos\left( \theta\right)}^{2}}}}} - {{{{\phi_R}}} \cdot {{\frac{1}{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}}}}} + {{{{\phi_R}}} \cdot {{\frac{1}{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}}} {{{cos\left( \theta\right)}^{2}}}} + {{{{{{\phi_L}}} \cdot {{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}}} - {{{{\phi_L}}} \cdot {{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}} {{{cos\left( \theta\right)}^{2}}}}} - {{{{\phi_R}}} \cdot {{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}}}} + {{{{\phi_R}}} \cdot {{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}} {{{cos\left( \theta\right)}^{2}}}}}{{{2}} {{({{{\phi_L}} - {{\phi_R}}})}}} & \frac{-{{{r}} {{sin\left( \theta\right)}} {{cos\left( \theta\right)}} {{({{{{{{{2}} {{{\phi_L}}}} - {{{{\phi_L}}} \cdot {{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}}}} - {{{{\phi_L}}} \cdot {{\frac{1}{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}}}}} - {{{2}} {{{\phi_R}}}}} + {{{{\phi_R}}} \cdot {{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}}} + {{{{\phi_R}}} \cdot {{\frac{1}{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}}}}})}}}}{{{2}} {{({{{\phi_L}} - {{\phi_R}}})}}} & \frac{{{r}} {{\frac{1}{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}}} {{({{{{\phi_L}} - {{{{\phi_L}}} \cdot {{{ⅇ}^{({{{2}} {{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}})}}}}} + {{{{{{\phi_L}}} \cdot {{{ⅇ}^{({{{2}} {{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}})}}} {{{cos\left( \theta\right)}^{2}}}} - {{{{\phi_L}}} \cdot {{{cos\left( \theta\right)}^{2}}}}} - {{\phi_R}}} + {{{{{\phi_R}}} \cdot {{{ⅇ}^{({{{2}} {{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}})}}}} - {{{{\phi_R}}} \cdot {{{ⅇ}^{({{{2}} {{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}})}}} {{{cos\left( \theta\right)}^{2}}}}} + {{{{\phi_R}}} \cdot {{{cos\left( \theta\right)}^{2}}}}})}}}{{{2}} {{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}} \\ 0 & \frac{{{cos\left( \theta\right)}} {{sin\left( \theta\right)}} {{({{{2} - {{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}} - {\frac{1}{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}}})}}}{-{{{2}} {{r}}}} & {\frac{1}{2}}{({{{2} - {{{2}} {{{cos\left( \theta\right)}^{2}}}}} + {{{\frac{1}{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}}} {{{cos\left( \theta\right)}^{2}}}} + {{{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}} {{{cos\left( \theta\right)}^{2}}}}})} & \frac{-{{{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}} {{cos\left( \theta\right)}} {{sin\left( \theta\right)}} {{({{{{{\phi_L}} - {{\phi_R}}} - {{{{\phi_L}}} \cdot {{\frac{1}{{ⅇ}^{({{{2}} {{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}})}}}}}} + {{{{\phi_R}}} \cdot {{\frac{1}{{ⅇ}^{({{{2}} {{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}})}}}}}})}}}}{{{2}} {{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}} \\ 0 & \frac{{{\frac{1}{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}}} {{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}} {{({{1} - {{ⅇ}^{({{{2}} {{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}})}}})}}}{{{2}} {{r}} {{({{{\phi_L}} - {{\phi_R}}})}}} & \frac{{{\frac{1}{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}}} {{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}} {{cos\left( \theta\right)}} {{({{1} - {{ⅇ}^{({{{2}} {{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}})}}})}}}{{{2}} {{sin\left( \theta\right)}} {{({{{\phi_L}} - {{\phi_R}}})}}} & {\frac{1}{2}}{({{{\frac{1}{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}}} {{({{1} + {{ⅇ}^{({{{2}} {{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}})}}})}}})}\end{matrix}\right]\right)} = {\left[\begin{matrix} 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0\end{matrix}\right]}$
${{\frac{\partial}{\partial r}}\left( \left[\begin{matrix} 1 & 0 & 0 & 0 \\ 0 & \frac{{{{{2}} {{{\phi_L}}} \cdot {{{cos\left( \theta\right)}^{2}}}} - {{{2}} {{{\phi_R}}} \cdot {{{cos\left( \theta\right)}^{2}}}}} + {{{{{{\phi_L}}} \cdot {{\frac{1}{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}}}} - {{{{\phi_L}}} \cdot {{\frac{1}{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}}} {{{cos\left( \theta\right)}^{2}}}}} - {{{{\phi_R}}} \cdot {{\frac{1}{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}}}}} + {{{{\phi_R}}} \cdot {{\frac{1}{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}}} {{{cos\left( \theta\right)}^{2}}}} + {{{{{{\phi_L}}} \cdot {{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}}} - {{{{\phi_L}}} \cdot {{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}} {{{cos\left( \theta\right)}^{2}}}}} - {{{{\phi_R}}} \cdot {{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}}}} + {{{{\phi_R}}} \cdot {{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}} {{{cos\left( \theta\right)}^{2}}}}}{{{2}} {{({{{\phi_L}} - {{\phi_R}}})}}} & \frac{-{{{r}} {{sin\left( \theta\right)}} {{cos\left( \theta\right)}} {{({{{{{{{2}} {{{\phi_L}}}} - {{{{\phi_L}}} \cdot {{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}}}} - {{{{\phi_L}}} \cdot {{\frac{1}{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}}}}} - {{{2}} {{{\phi_R}}}}} + {{{{\phi_R}}} \cdot {{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}}} + {{{{\phi_R}}} \cdot {{\frac{1}{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}}}}})}}}}{{{2}} {{({{{\phi_L}} - {{\phi_R}}})}}} & \frac{{{r}} {{\frac{1}{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}}} {{({{{{\phi_L}} - {{{{\phi_L}}} \cdot {{{ⅇ}^{({{{2}} {{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}})}}}}} + {{{{{{\phi_L}}} \cdot {{{ⅇ}^{({{{2}} {{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}})}}} {{{cos\left( \theta\right)}^{2}}}} - {{{{\phi_L}}} \cdot {{{cos\left( \theta\right)}^{2}}}}} - {{\phi_R}}} + {{{{{\phi_R}}} \cdot {{{ⅇ}^{({{{2}} {{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}})}}}} - {{{{\phi_R}}} \cdot {{{ⅇ}^{({{{2}} {{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}})}}} {{{cos\left( \theta\right)}^{2}}}}} + {{{{\phi_R}}} \cdot {{{cos\left( \theta\right)}^{2}}}}})}}}{{{2}} {{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}} \\ 0 & \frac{{{cos\left( \theta\right)}} {{sin\left( \theta\right)}} {{({{{2} - {{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}} - {\frac{1}{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}}})}}}{-{{{2}} {{r}}}} & {\frac{1}{2}}{({{{2} - {{{2}} {{{cos\left( \theta\right)}^{2}}}}} + {{{\frac{1}{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}}} {{{cos\left( \theta\right)}^{2}}}} + {{{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}} {{{cos\left( \theta\right)}^{2}}}}})} & \frac{-{{{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}} {{cos\left( \theta\right)}} {{sin\left( \theta\right)}} {{({{{{{\phi_L}} - {{\phi_R}}} - {{{{\phi_L}}} \cdot {{\frac{1}{{ⅇ}^{({{{2}} {{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}})}}}}}} + {{{{\phi_R}}} \cdot {{\frac{1}{{ⅇ}^{({{{2}} {{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}})}}}}}})}}}}{{{2}} {{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}} \\ 0 & \frac{{{\frac{1}{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}}} {{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}} {{({{1} - {{ⅇ}^{({{{2}} {{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}})}}})}}}{{{2}} {{r}} {{({{{\phi_L}} - {{\phi_R}}})}}} & \frac{{{\frac{1}{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}}} {{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}} {{cos\left( \theta\right)}} {{({{1} - {{ⅇ}^{({{{2}} {{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}})}}})}}}{{{2}} {{sin\left( \theta\right)}} {{({{{\phi_L}} - {{\phi_R}}})}}} & {\frac{1}{2}}{({{{\frac{1}{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}}} {{({{1} + {{ⅇ}^{({{{2}} {{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}})}}})}}})}\end{matrix}\right]\right)} = {\left[\begin{matrix} 0 & 0 & 0 & 0 \\ 0 & 0 & \frac{-{{{cos\left( \theta\right)}} {{sin\left( \theta\right)}} {{({{{{{2}} {{{\phi_L}}}} - {{{2}} {{{\phi_R}}}}} + {{{{\phi_R}}} \cdot {{\frac{1}{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}}}} + {{{{{{\phi_R}}} \cdot {{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}}} - {{{{\phi_L}}} \cdot {{\frac{1}{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}}}}} - {{{{\phi_L}}} \cdot {{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}}}}})}}}}{{{2}} {{({{{\phi_L}} - {{\phi_R}}})}}} & \frac{{{ⅈ}} \cdot {{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}} {{({{{{\phi_L}} - {{{{\phi_L}}} \cdot {{\frac{1}{{ⅇ}^{({{{2}} {{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}})}}}}}} + {{{{{{\phi_L}}} \cdot {{\frac{1}{{ⅇ}^{({{{2}} {{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}})}}}} {{{cos\left( \theta\right)}^{2}}}} - {{{{\phi_L}}} \cdot {{{cos\left( \theta\right)}^{2}}}}} - {{\phi_R}}} + {{{{{\phi_R}}} \cdot {{\frac{1}{{ⅇ}^{({{{2}} {{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}})}}}}} - {{{{\phi_R}}} \cdot {{\frac{1}{{ⅇ}^{({{{2}} {{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}})}}}} {{{cos\left( \theta\right)}^{2}}}}} + {{{{\phi_R}}} \cdot {{{cos\left( \theta\right)}^{2}}}}})}}}{{{2}} {{({{{\phi_L}} - {{\phi_R}}})}}} \\ 0 & \frac{{{cos\left( \theta\right)}} {{sin\left( \theta\right)}} {{({{{2} - {\frac{1}{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}}} - {{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}})}}}{{{2}} {{{r}^{2}}}} & 0 & 0 \\ 0 & \frac{-{{{\frac{1}{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}}} {{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}} {{({{1} - {{ⅇ}^{({{{2}} {{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}})}}})}}}}{{{2}} {{{r}^{2}}} {{({{{\phi_L}} - {{\phi_R}}})}}} & 0 & 0\end{matrix}\right]}$
${{\frac{\partial}{\partial \theta}}\left( \left[\begin{matrix} 1 & 0 & 0 & 0 \\ 0 & \frac{{{{{2}} {{{\phi_L}}} \cdot {{{cos\left( \theta\right)}^{2}}}} - {{{2}} {{{\phi_R}}} \cdot {{{cos\left( \theta\right)}^{2}}}}} + {{{{{{\phi_L}}} \cdot {{\frac{1}{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}}}} - {{{{\phi_L}}} \cdot {{\frac{1}{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}}} {{{cos\left( \theta\right)}^{2}}}}} - {{{{\phi_R}}} \cdot {{\frac{1}{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}}}}} + {{{{\phi_R}}} \cdot {{\frac{1}{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}}} {{{cos\left( \theta\right)}^{2}}}} + {{{{{{\phi_L}}} \cdot {{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}}} - {{{{\phi_L}}} \cdot {{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}} {{{cos\left( \theta\right)}^{2}}}}} - {{{{\phi_R}}} \cdot {{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}}}} + {{{{\phi_R}}} \cdot {{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}} {{{cos\left( \theta\right)}^{2}}}}}{{{2}} {{({{{\phi_L}} - {{\phi_R}}})}}} & \frac{-{{{r}} {{sin\left( \theta\right)}} {{cos\left( \theta\right)}} {{({{{{{{{2}} {{{\phi_L}}}} - {{{{\phi_L}}} \cdot {{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}}}} - {{{{\phi_L}}} \cdot {{\frac{1}{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}}}}} - {{{2}} {{{\phi_R}}}}} + {{{{\phi_R}}} \cdot {{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}}} + {{{{\phi_R}}} \cdot {{\frac{1}{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}}}}})}}}}{{{2}} {{({{{\phi_L}} - {{\phi_R}}})}}} & \frac{{{r}} {{\frac{1}{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}}} {{({{{{\phi_L}} - {{{{\phi_L}}} \cdot {{{ⅇ}^{({{{2}} {{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}})}}}}} + {{{{{{\phi_L}}} \cdot {{{ⅇ}^{({{{2}} {{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}})}}} {{{cos\left( \theta\right)}^{2}}}} - {{{{\phi_L}}} \cdot {{{cos\left( \theta\right)}^{2}}}}} - {{\phi_R}}} + {{{{{\phi_R}}} \cdot {{{ⅇ}^{({{{2}} {{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}})}}}} - {{{{\phi_R}}} \cdot {{{ⅇ}^{({{{2}} {{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}})}}} {{{cos\left( \theta\right)}^{2}}}}} + {{{{\phi_R}}} \cdot {{{cos\left( \theta\right)}^{2}}}}})}}}{{{2}} {{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}} \\ 0 & \frac{{{cos\left( \theta\right)}} {{sin\left( \theta\right)}} {{({{{2} - {{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}} - {\frac{1}{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}}})}}}{-{{{2}} {{r}}}} & {\frac{1}{2}}{({{{2} - {{{2}} {{{cos\left( \theta\right)}^{2}}}}} + {{{\frac{1}{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}}} {{{cos\left( \theta\right)}^{2}}}} + {{{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}} {{{cos\left( \theta\right)}^{2}}}}})} & \frac{-{{{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}} {{cos\left( \theta\right)}} {{sin\left( \theta\right)}} {{({{{{{\phi_L}} - {{\phi_R}}} - {{{{\phi_L}}} \cdot {{\frac{1}{{ⅇ}^{({{{2}} {{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}})}}}}}} + {{{{\phi_R}}} \cdot {{\frac{1}{{ⅇ}^{({{{2}} {{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}})}}}}}})}}}}{{{2}} {{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}} \\ 0 & \frac{{{\frac{1}{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}}} {{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}} {{({{1} - {{ⅇ}^{({{{2}} {{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}})}}})}}}{{{2}} {{r}} {{({{{\phi_L}} - {{\phi_R}}})}}} & \frac{{{\frac{1}{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}}} {{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}} {{cos\left( \theta\right)}} {{({{1} - {{ⅇ}^{({{{2}} {{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}})}}})}}}{{{2}} {{sin\left( \theta\right)}} {{({{{\phi_L}} - {{\phi_R}}})}}} & {\frac{1}{2}}{({{{\frac{1}{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}}} {{({{1} + {{ⅇ}^{({{{2}} {{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}})}}})}}})}\end{matrix}\right]\right)} = {\left[\begin{matrix} 0 & 0 & 0 & 0 \\ 0 & \frac{-{{{sin\left( \theta\right)}} {{cos\left( \theta\right)}} {{({{{{{2}} {{{\phi_L}}}} - {{{2}} {{{\phi_R}}}}} + {{{{\phi_R}}} \cdot {{\frac{1}{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}}}} + {{{{{{\phi_R}}} \cdot {{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}}} - {{{{\phi_L}}} \cdot {{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}}}} - {{{{\phi_L}}} \cdot {{\frac{1}{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}}}}}})}}}}{{{\phi_L}} - {{\phi_R}}} & \frac{{{r}} {{({{{{{{{2}} {{{\phi_L}}}} - {{{4}} {{{\phi_L}}} \cdot {{{cos\left( \theta\right)}^{2}}}}} - {{{{\phi_L}}} \cdot {{\frac{1}{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}}}}} - {{{{\phi_L}}} \cdot {{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}}}} + {{{2}} {{{\phi_L}}} \cdot {{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}} {{{cos\left( \theta\right)}^{2}}}} + {{{{2}} {{{\phi_L}}} \cdot {{\frac{1}{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}}} {{{cos\left( \theta\right)}^{2}}}} - {{{2}} {{{\phi_R}}}}} + {{{4}} {{{\phi_R}}} \cdot {{{cos\left( \theta\right)}^{2}}}} + {{{{\phi_R}}} \cdot {{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}}} + {{{{{{\phi_R}}} \cdot {{\frac{1}{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}}}} - {{{2}} {{{\phi_R}}} \cdot {{\frac{1}{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}}} {{{cos\left( \theta\right)}^{2}}}}} - {{{2}} {{{\phi_R}}} \cdot {{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}} {{{cos\left( \theta\right)}^{2}}}}}})}}}{{{2}} {{({{{\phi_L}} - {{\phi_R}}})}}} & \frac{-{{{r}} {{ⅈ}} \cdot {{\frac{1}{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}}} {{sin\left( \theta\right)}} {{cos\left( \theta\right)}} {{({{{{{\phi_L}} - {{\phi_R}}} - {{{{\phi_L}}} \cdot {{{ⅇ}^{({{{2}} {{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}})}}}}} + {{{{\phi_R}}} \cdot {{{ⅇ}^{({{{2}} {{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}})}}}}})}}}}{{{\phi_L}} - {{\phi_R}}} \\ 0 & \frac{{{{{2} - {{{4}} {{{cos\left( \theta\right)}^{2}}}}} - {{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}} - {\frac{1}{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}}} + {{{2}} {{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}} {{{cos\left( \theta\right)}^{2}}}} + {{{2}} \cdot {{\frac{1}{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}}} {{{cos\left( \theta\right)}^{2}}}}}{{{2}} {{r}}} & {{cos\left( \theta\right)}} {{sin\left( \theta\right)}} {{({{{2} - {\frac{1}{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}}} - {{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}})}} & \frac{{{\frac{1}{\sqrt{-{1}}}}} {{\frac{1}{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}}} {{({{{\phi_L}} + {{{2}} {{{\phi_L}}} \cdot {{{ⅇ}^{({{{2}} {{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}})}}}} + {{{2}} {{{\phi_L}}} \cdot {{ {-{1}} {{\sqrt{-{1}}}}}} {{{ⅇ}^{({{{2}} {{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}})}}} {{{cos\left( \theta\right)}^{2}}}} + {{{{\phi_L}}} \cdot {{ⅈ}} \cdot {{{{{( -{1})}^{2}}} {{\sqrt{-{1}}}}}} {{{ⅇ}^{({{{2}} {{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}})}}}} + {{{2}} {{{\phi_L}}} \cdot {{ⅈ}} \cdot {{{{{( -{1})}^{2}}} {{\sqrt{-{1}}}}}}} + {{{2}} {{{\phi_L}}} \cdot {{ⅈ}} \cdot {{{{{( -{1})}^{3}}} {{\sqrt{-{1}}}}}} {{{cos\left( \theta\right)}^{2}}}} + {{{{\phi_R}}} \cdot {{{ⅇ}^{({{{2}} {{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}})}}}} + {{{2}} {{{\phi_R}}}} + {{{2}} {{{\phi_R}}} \cdot {{{{{( -{1})}^{5}}} {{\sqrt{-{1}}}}}} {{{cos\left( \theta\right)}^{2}}}} + {{{{\phi_R}}} \cdot {{ⅈ}} \cdot {{{{{( -{1})}^{6}}} {{\sqrt{-{1}}}}}}} + {{{2}} {{{\phi_R}}} \cdot {{ⅈ}} \cdot {{{{{( -{1})}^{6}}} {{\sqrt{-{1}}}}}} {{{ⅇ}^{({{{2}} {{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}})}}}} + {{{2}} {{{\phi_R}}} \cdot {{ⅈ}} \cdot {{{{{( -{1})}^{7}}} {{\sqrt{-{1}}}}}} {{{ⅇ}^{({{{2}} {{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}})}}} {{{cos\left( \theta\right)}^{2}}}}})}}}{{{2}} {{({{{\phi_L}} - {{\phi_R}}})}}} \\ 0 & 0 & \frac{-{{{ⅈ}} \cdot {{\frac{1}{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}}} {{({{{{\phi_L}} - {{{{\phi_L}}} \cdot {{{ⅇ}^{({{{2}} {{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}})}}}}} + {{{{{\phi_R}}} \cdot {{{ⅇ}^{({{{2}} {{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}})}}}} - {{\phi_R}}}})}}}}{{{2}} {{({{{{{\phi_L}} - {{{{\phi_L}}} \cdot {{{cos\left( \theta\right)}^{2}}}}} - {{\phi_R}}} + {{{{\phi_R}}} \cdot {{{cos\left( \theta\right)}^{2}}}}})}}} & 0\end{matrix}\right]}$
${{\frac{\partial}{\partial \phi}}\left( \left[\begin{matrix} 1 & 0 & 0 & 0 \\ 0 & \frac{{{{{2}} {{{\phi_L}}} \cdot {{{cos\left( \theta\right)}^{2}}}} - {{{2}} {{{\phi_R}}} \cdot {{{cos\left( \theta\right)}^{2}}}}} + {{{{{{\phi_L}}} \cdot {{\frac{1}{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}}}} - {{{{\phi_L}}} \cdot {{\frac{1}{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}}} {{{cos\left( \theta\right)}^{2}}}}} - {{{{\phi_R}}} \cdot {{\frac{1}{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}}}}} + {{{{\phi_R}}} \cdot {{\frac{1}{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}}} {{{cos\left( \theta\right)}^{2}}}} + {{{{{{\phi_L}}} \cdot {{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}}} - {{{{\phi_L}}} \cdot {{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}} {{{cos\left( \theta\right)}^{2}}}}} - {{{{\phi_R}}} \cdot {{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}}}} + {{{{\phi_R}}} \cdot {{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}} {{{cos\left( \theta\right)}^{2}}}}}{{{2}} {{({{{\phi_L}} - {{\phi_R}}})}}} & \frac{-{{{r}} {{sin\left( \theta\right)}} {{cos\left( \theta\right)}} {{({{{{{{{2}} {{{\phi_L}}}} - {{{{\phi_L}}} \cdot {{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}}}} - {{{{\phi_L}}} \cdot {{\frac{1}{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}}}}} - {{{2}} {{{\phi_R}}}}} + {{{{\phi_R}}} \cdot {{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}}} + {{{{\phi_R}}} \cdot {{\frac{1}{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}}}}})}}}}{{{2}} {{({{{\phi_L}} - {{\phi_R}}})}}} & \frac{{{r}} {{\frac{1}{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}}} {{({{{{\phi_L}} - {{{{\phi_L}}} \cdot {{{ⅇ}^{({{{2}} {{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}})}}}}} + {{{{{{\phi_L}}} \cdot {{{ⅇ}^{({{{2}} {{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}})}}} {{{cos\left( \theta\right)}^{2}}}} - {{{{\phi_L}}} \cdot {{{cos\left( \theta\right)}^{2}}}}} - {{\phi_R}}} + {{{{{\phi_R}}} \cdot {{{ⅇ}^{({{{2}} {{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}})}}}} - {{{{\phi_R}}} \cdot {{{ⅇ}^{({{{2}} {{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}})}}} {{{cos\left( \theta\right)}^{2}}}}} + {{{{\phi_R}}} \cdot {{{cos\left( \theta\right)}^{2}}}}})}}}{{{2}} {{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}} \\ 0 & \frac{{{cos\left( \theta\right)}} {{sin\left( \theta\right)}} {{({{{2} - {{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}} - {\frac{1}{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}}})}}}{-{{{2}} {{r}}}} & {\frac{1}{2}}{({{{2} - {{{2}} {{{cos\left( \theta\right)}^{2}}}}} + {{{\frac{1}{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}}} {{{cos\left( \theta\right)}^{2}}}} + {{{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}} {{{cos\left( \theta\right)}^{2}}}}})} & \frac{-{{{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}} {{cos\left( \theta\right)}} {{sin\left( \theta\right)}} {{({{{{{\phi_L}} - {{\phi_R}}} - {{{{\phi_L}}} \cdot {{\frac{1}{{ⅇ}^{({{{2}} {{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}})}}}}}} + {{{{\phi_R}}} \cdot {{\frac{1}{{ⅇ}^{({{{2}} {{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}})}}}}}})}}}}{{{2}} {{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}} \\ 0 & \frac{{{\frac{1}{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}}} {{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}} {{({{1} - {{ⅇ}^{({{{2}} {{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}})}}})}}}{{{2}} {{r}} {{({{{\phi_L}} - {{\phi_R}}})}}} & \frac{{{\frac{1}{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}}} {{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}} {{cos\left( \theta\right)}} {{({{1} - {{ⅇ}^{({{{2}} {{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}})}}})}}}{{{2}} {{sin\left( \theta\right)}} {{({{{\phi_L}} - {{\phi_R}}})}}} & {\frac{1}{2}}{({{{\frac{1}{{ⅇ}^{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}}} {{({{1} + {{ⅇ}^{({{{2}} {{\sqrt{{-{{{\phi_L}}^{2}}} + {{{{2}} {{{\phi_L}}} \cdot {{{\phi_R}}}} - {{{\phi_R}}^{2}}}}}}})}}})}}})}\end{matrix}\right]\right)} = {\left[\begin{matrix} 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0\end{matrix}\right]}$
volume element: ${{ⅈ}} \cdot {{{r}^{2}}} {{sin\left( \theta\right)}}$
volume integral: ${{{\frac{1}{3}}{({-{{{\Delta (cos(\theta))}} \cdot {{{\Delta (r^3)}}} \cdot {{\Delta t}} \cdot {{ⅈ}}}})}}} {{\Delta \phi}}$
finite volume (0,0)-form:
${{u(x_C, t_R)}} = {{{u(x_C, t_L)}} + {{{\Delta t}} \cdot {{({{{{{\frac{1}{{\mathcal{V}(x_C)}}}{({1})}}} {{({{{{-{({\int\limits_{{{\phi_L}}}^{{{\phi_R}}}d \phi\left({\int\limits_{{{\theta_L}}}^{{{\theta_R}}}d \theta\left({\int\limits_{{{r_L}}}^{{{r_R}}}d r\left({{{{{J(t_R)}}} \cdot {{{{e_{t}}^{\bar{t}}(t_R)}}} \cdot {{{F^{t}(t_R)}}}} - {{{{J(t_L)}}} \cdot {{{{e_{t}}^{\bar{t}}(t_L)}}} \cdot {{{F^{t}(t_L)}}}}}\right)}\right)}\right)})}} - {({\int\limits_{{{\phi_L}}}^{{{\phi_R}}}d \phi\left({\int\limits_{{{\theta_L}}}^{{{\theta_R}}}d \theta\left({\int\limits_{{{t_L}}}^{{{t_R}}}d t\left({{{{{J(r_R)}}} \cdot {{{{e_{r}}^{\bar{r}}(r_R)}}} \cdot {{{F^{r}(r_R)}}}} - {{{{J(r_L)}}} \cdot {{{{e_{r}}^{\bar{r}}(r_L)}}} \cdot {{{F^{r}(r_L)}}}}}\right)}\right)}\right)})}} - {({\int\limits_{{{\phi_L}}}^{{{\phi_R}}}d \phi\left({\int\limits_{{{r_L}}}^{{{r_R}}}d r\left({\int\limits_{{{t_L}}}^{{{t_R}}}d t\left({{{{{J(\theta_R)}}} \cdot {{{{e_{\theta}}^{\bar{\theta}}(\theta_R)}}} \cdot {{{F^{\theta}(\theta_R)}}}} - {{{{J(\theta_L)}}} \cdot {{{{e_{\theta}}^{\bar{\theta}}(\theta_L)}}} \cdot {{{F^{\theta}(\theta_L)}}}}}\right)}\right)}\right)})}} - {({\int\limits_{{{\theta_L}}}^{{{\theta_R}}}d \theta\left({\int\limits_{{{r_L}}}^{{{r_R}}}d r\left({\int\limits_{{{t_L}}}^{{{t_R}}}d t\left({{{{{J(\phi_R)}}} \cdot {{{{e_{\phi}}^{\bar{\phi}}(\phi_R)}}} \cdot {{{F^{\phi}(\phi_R)}}}} - {{{{J(\phi_L)}}} \cdot {{{{e_{\phi}}^{\bar{\phi}}(\phi_L)}}} \cdot {{{F^{\phi}(\phi_L)}}}}}\right)}\right)}\right)})}})}}} + {{S(x_C)}}})}}}}$
${{u(x_C, t_R)}} = {{{u(x_C, t_L)}} + {{{\Delta t}} \cdot {{({{{{\frac{1}{{{{\frac{1}{3}}{({-{{{\Delta (cos(\theta))}} \cdot {{{\Delta (r^3)}}} \cdot {{\Delta t}} \cdot {{ⅈ}}}})}}} {{\Delta \phi}}}}} {{({{{{-{({\int\limits_{{{\phi_L}}}^{{{\phi_R}}}d \phi\left({\int\limits_{{{\theta_L}}}^{{{\theta_R}}}d \theta\left({\int\limits_{{{r_L}}}^{{{r_R}}}d r\left({{{{ⅈ}} \cdot {{{r}^{2}}} {{sin\left( \theta\right)}} {{{F^{t}(t_R)}}}} - {{{ⅈ}} \cdot {{{r}^{2}}} {{sin\left( \theta\right)}} {{{F^{t}(t_L)}}}}}\right)}\right)}\right)})}} - {({\int\limits_{{{\phi_L}}}^{{{\phi_R}}}d \phi\left({\int\limits_{{{\theta_L}}}^{{{\theta_R}}}d \theta\left({\int\limits_{{{t_L}}}^{{{t_R}}}d t\left({{{{ⅈ}} \cdot {{{{r_R}}^{2}}} {{sin\left( \theta\right)}} {{{F^{r}(r_R)}}}} - {{{ⅈ}} \cdot {{{{r_L}}^{2}}} {{sin\left( \theta\right)}} {{{F^{r}(r_L)}}}}}\right)}\right)}\right)})}} - {({\int\limits_{{{\phi_L}}}^{{{\phi_R}}}d \phi\left({\int\limits_{{{r_L}}}^{{{r_R}}}d r\left({\int\limits_{{{t_L}}}^{{{t_R}}}d t\left({{{{ⅈ}} \cdot {{{r}^{2}}} {{sin\left( {\theta_R}\right)}} {{{F^{\theta}(\theta_R)}}}} - {{{ⅈ}} \cdot {{{r}^{2}}} {{sin\left( {\theta_L}\right)}} {{{F^{\theta}(\theta_L)}}}}}\right)}\right)}\right)})}} - {({\int\limits_{{{\theta_L}}}^{{{\theta_R}}}d \theta\left({\int\limits_{{{r_L}}}^{{{r_R}}}d r\left({\int\limits_{{{t_L}}}^{{{t_R}}}d t\left({{{{ⅈ}} \cdot {{{r}^{2}}} {{sin\left( \theta\right)}} {{{F^{\phi}(\phi_R)}}}} - {{{ⅈ}} \cdot {{{r}^{2}}} {{sin\left( \theta\right)}} {{{F^{\phi}(\phi_L)}}}}}\right)}\right)}\right)})}})}}} + {{S(x_C)}}})}}}}$
${{u(x_C, t_R)}} = {{{u(x_C, t_L)}} + {{{\Delta t}} \cdot {{({{{{\frac{1}{{{{\frac{1}{3}}{({-{{{\Delta (cos(\theta))}} \cdot {{{\Delta (r^3)}}} \cdot {{\Delta t}} \cdot {{ⅈ}}}})}}} {{\Delta \phi}}}}} {{({{{{-{{{{\frac{1}{3}}{({-{{{{\Delta (r^3)}}} \cdot {{ⅈ}} \cdot {{({{{{{F^{t}(t_L)}}} \cdot {{cos\left( {\theta_L}\right)}}} + {{{{{{F^{t}(t_R)}}} \cdot {{cos\left( {\theta_R}\right)}}} - {{{{F^{t}(t_L)}}} \cdot {{cos\left( {\theta_R}\right)}}}} - {{{{F^{t}(t_R)}}} \cdot {{cos\left( {\theta_L}\right)}}}}})}}}})}}} {{\Delta \phi}}}} - { {-{{{\Delta t}} \cdot {{ⅈ}} \cdot {{({{{{{F^{r}(r_L)}}} \cdot {{{{r_L}}^{2}}} {{cos\left( {\theta_L}\right)}}} + {{{{F^{r}(r_R)}}} \cdot {{{\Delta (r^2)}}} \cdot {{cos\left( {\theta_R}\right)}}} + {{{{{{{F^{r}(r_R)}}} \cdot {{{{r_L}}^{2}}} {{cos\left( {\theta_R}\right)}}} - {{{{F^{r}(r_L)}}} \cdot {{{{r_L}}^{2}}} {{cos\left( {\theta_R}\right)}}}} - {{{{F^{r}(r_R)}}} \cdot {{{\Delta (r^2)}}} \cdot {{cos\left( {\theta_L}\right)}}}} - {{{{F^{r}(r_R)}}} \cdot {{{{r_L}}^{2}}} {{cos\left( {\theta_L}\right)}}}}})}}}} {{\Delta \phi}}}} - {{{{\frac{1}{3}}{({-{{{{\Delta (r^3)}}} \cdot {{\Delta t}} \cdot {{ⅈ}} \cdot {{({{{{{F^{\theta}(\theta_L)}}} \cdot {{sin\left( {\theta_L}\right)}}} - {{{{F^{\theta}(\theta_R)}}} \cdot {{sin\left( {\theta_R}\right)}}}})}}}})}}} {{\Delta \phi}}}} - {{\frac{1}{3}}{({-{{{{\Delta (r^3)}}} \cdot {{\Delta t}} \cdot {{ⅈ}} \cdot {{({{{{{{{F^{\phi}(\phi_L)}}} \cdot {{cos\left( {\theta_L}\right)}}} - {{{{F^{\phi}(\phi_L)}}} \cdot {{cos\left( {\theta_R}\right)}}}} - {{{{F^{\phi}(\phi_R)}}} \cdot {{cos\left( {\theta_L}\right)}}}} + {{{{F^{\phi}(\phi_R)}}} \cdot {{cos\left( {\theta_R}\right)}}}})}}}})}}})}}} + {{S(x_C)}}})}}}}$
${{u(x_C, t_R)}} = {{{{{\frac{1}{-1}}{({1})}}} {{{F^{\phi}(\phi_L)}}} \cdot {{\Delta t}} \cdot {{cos\left( {\theta_L}\right)}} {{{\frac{1}{\Delta (cos(\theta))}}{({1})}}} {{{\frac{1}{\Delta \phi}}{({1})}}}} + {{{{F^{\phi}(\phi_L)}}} \cdot {{\Delta t}} \cdot {{cos\left( {\theta_R}\right)}} {{{\frac{1}{\Delta (cos(\theta))}}{({1})}}} {{{\frac{1}{\Delta \phi}}{({1})}}}} + {{{{F^{\phi}(\phi_R)}}} \cdot {{\Delta t}} \cdot {{cos\left( {\theta_L}\right)}} {{{\frac{1}{\Delta (cos(\theta))}}{({1})}}} {{{\frac{1}{\Delta \phi}}{({1})}}}} + {{{{\frac{1}{-1}}{({1})}}} {{{F^{\phi}(\phi_R)}}} \cdot {{\Delta t}} \cdot {{cos\left( {\theta_R}\right)}} {{{\frac{1}{\Delta (cos(\theta))}}{({1})}}} {{{\frac{1}{\Delta \phi}}{({1})}}}} + {{{{F^{\theta}(\theta_R)}}} \cdot {{\Delta t}} \cdot {{sin\left( {\theta_R}\right)}} {{{\frac{1}{\Delta (cos(\theta))}}{({1})}}}} + {{{3}} \cdot {{{\frac{1}{-1}}{({1})}}} {{{F^{r}(r_L)}}} \cdot {{\Delta t}} \cdot {{{{r_L}}^{2}}} {{cos\left( {\theta_L}\right)}} {{{\frac{1}{\Delta (cos(\theta))}}{({1})}}} {{{\frac{1}{{\Delta (r^3)}}}{({1})}}}} + {{{3}} {{{F^{r}(r_L)}}} \cdot {{\Delta t}} \cdot {{{{r_L}}^{2}}} {{cos\left( {\theta_R}\right)}} {{{\frac{1}{\Delta (cos(\theta))}}{({1})}}} {{{\frac{1}{{\Delta (r^3)}}}{({1})}}}} + {{{3}} {{{F^{r}(r_R)}}} \cdot {{{\Delta (r^2)}}} \cdot {{\Delta t}} \cdot {{cos\left( {\theta_L}\right)}} {{{\frac{1}{\Delta (cos(\theta))}}{({1})}}} {{{\frac{1}{{\Delta (r^3)}}}{({1})}}}} + {{{3}} \cdot {{{\frac{1}{-1}}{({1})}}} {{{F^{r}(r_R)}}} \cdot {{{\Delta (r^2)}}} \cdot {{\Delta t}} \cdot {{cos\left( {\theta_R}\right)}} {{{\frac{1}{\Delta (cos(\theta))}}{({1})}}} {{{\frac{1}{{\Delta (r^3)}}}{({1})}}}} + {{{3}} {{{F^{r}(r_R)}}} \cdot {{\Delta t}} \cdot {{{{r_L}}^{2}}} {{cos\left( {\theta_L}\right)}} {{{\frac{1}{\Delta (cos(\theta))}}{({1})}}} {{{\frac{1}{{\Delta (r^3)}}}{({1})}}}} + {{{3}} \cdot {{{\frac{1}{-1}}{({1})}}} {{{F^{r}(r_R)}}} \cdot {{\Delta t}} \cdot {{{{r_L}}^{2}}} {{cos\left( {\theta_R}\right)}} {{{\frac{1}{\Delta (cos(\theta))}}{({1})}}} {{{\frac{1}{{\Delta (r^3)}}}{({1})}}}} + {{{{\frac{1}{-1}}{({1})}}} {{{F^{t}(t_L)}}} \cdot {{cos\left( {\theta_L}\right)}} {{{\frac{1}{\Delta (cos(\theta))}}{({1})}}}} + {{{{F^{t}(t_L)}}} \cdot {{cos\left( {\theta_R}\right)}} {{{\frac{1}{\Delta (cos(\theta))}}{({1})}}}} + {{{{F^{t}(t_R)}}} \cdot {{cos\left( {\theta_L}\right)}} {{{\frac{1}{\Delta (cos(\theta))}}{({1})}}}} + {{{{\frac{1}{-1}}{({1})}}} {{{F^{t}(t_R)}}} \cdot {{cos\left( {\theta_R}\right)}} {{{\frac{1}{\Delta (cos(\theta))}}{({1})}}}} + {{{{S(x_C)}}} \cdot {{\Delta t}}} + {{u(x_C, t_L)}} + {{{{\frac{1}{-1}}{({1})}}} {{{F^{\theta}(\theta_L)}}} \cdot {{\Delta t}} \cdot {{sin\left( {\theta_L}\right)}} {{{\frac{1}{\Delta (cos(\theta))}}{({1})}}}}}$