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{\displaystyle {\begin{aligned}&{\frac {\left(i^{2}-2\right)}{2\left(1+i^{2}\right)}}(b\ )+{\frac {i\left(i^{2}-1\right)}{\left(1+i^{2}\right)^{2}}}\left({\frac {db}{dq}}\right)+{\frac {3i}{2\left(1+i^{2}\right)}}\\&\qquad \times \left({\frac {b_{1}}{2}}\right)-{\frac {i^{2}\left(i^{2}-1\right)}{\left(1+i^{2}\right)^{2}}}\left({\frac {db_{1}}{2dq}}\right)=\mathrm {G} ,\\&{\frac {\left(i^{2}-2\right)}{2\left(1+i^{2}\right)}}(b_{1})+{\frac {i\left(i^{2}-1\right)}{\left(1+i^{2}\right)^{2}}}\left({\frac {db_{1}}{dq}}\right)+{\frac {3i}{2\left(1+i^{2}\right)}}\\&\qquad \times \left[\quad (b\ )+{\frac {1}{2}}(b_{2})\right]-{\frac {i^{2}\left(i^{2}-1\right)}{\left(1+i^{2}\right)^{2}}}\left[\quad {\frac {db}{dq}}\ +{\frac {1}{2}}\left({\frac {db_{2}}{dq}}\right)\right]=\sideset {^{1}}{}{\mathrm {G} },\\&{\frac {\left(i^{2}-2\right)}{2\left(1+i^{2}\right)}}(b_{2})+{\frac {i\left(i^{2}-1\right)}{\left(1+i^{2}\right)^{2}}}\left({\frac {db_{2}}{dq}}\right)+{\frac {3i}{2\left(1+i^{2}\right)}}\\&\qquad \times \left[{\frac {1}{2}}(b_{1})+{\frac {1}{2}}(b_{3})\right]-{\frac {i^{2}\left(i^{2}-1\right)}{\left(1+i^{2}\right)^{2}}}\left[{\frac {1}{2}}{\frac {db_{1}}{dq}}+{\frac {1}{2}}\left({\frac {db_{3}}{dq}}\right)\right]=\sideset {^{2}}{}{\mathrm {G} },\\&\ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \,;\\\\&{\frac {3i^{2}}{2\left(1+i^{2}\right)}}(b\ )+{\frac {i\left(i^{2}-1\right)}{\left(1+i^{2}\right)^{2}}}\left({\frac {db}{dq}}\right)+{\frac {i\left(1-2i^{2}\right)}{2\left(1+i^{2}\right)}}\\&\qquad \times \left({\frac {b_{1}}{2}}\right)-{\frac {i^{2}\left(i^{2}-1\right)}{\left(1+i^{2}\right)^{2}}}\left({\frac {db_{1}}{2dq}}\right)=\mathrm {H} ,\\&{\frac {3i^{2}}{2\left(1+i^{2}\right)}}(b_{1})+{\frac {i\left(i^{2}-1\right)}{\left(1+i^{2}\right)^{2}}}\left({\frac {db_{1}}{dq}}\right)+{\frac {i\left(1-2i^{2}\right)}{2\left(1+i^{2}\right)}}\\&\qquad \times \left[\quad (b)\ +{\frac {1}{2}}(b_{2})\right]-{\frac {i^{2}\left(i^{2}-1\right)}{\left(1+i^{2}\right)^{2}}}\left[\quad {\frac {db}{dq}}\ +{\frac {1}{2}}\left({\frac {db_{2}}{dq}}\right)\right]=\sideset {^{1}}{}{\mathrm {H} },\\&{\frac {3i^{2}}{2\left(1+i^{2}\right)}}(b_{2})+{\frac {i\left(i^{2}-1\right)}{\left(1+i^{2}\right)^{2}}}\left({\frac {db_{2}}{dq}}\right)+{\frac {i\left(1-2i^{2}\right)}{2\left(1+i^{2}\right)}}\\&\qquad \times \left[{\frac {1}{2}}(b_{1})+{\frac {1}{2}}(b_{3})\right]-{\frac {i^{2}\left(i^{2}-1\right)}{\left(1+i^{2}\right)^{2}}}\left[{\frac {1}{2}}{\frac {db_{1}}{dq}}+{\frac {1}{2}}\left({\frac {db_{3}}{dq}}\right)\right]=\sideset {^{2}}{}{\mathrm {H} },\\&\ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \,;\end{aligned}}}
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{\displaystyle {\frac {a^{2}\left[r-r'\cos(\varphi '-\varphi )\right]}{\sideset {^{1}}{^{3}}v}}=}
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{\displaystyle {\begin{aligned}\mathrm {F} &+\quad \sideset {^{1}}{}{\mathrm {F} }\cos \ \ (n't-nt+\mathrm {B} )\\&+{\frac {1}{2}}\sideset {^{2}}{}{\mathrm {F} }\cos 2(n't-nt+\mathrm {B} )\\&+{\frac {1}{3}}\sideset {^{3}}{}{\mathrm {F} }\cos 3(n't-nt+\mathrm {B} )\\&+\ldots \ldots \ldots \ldots \ldots \ldots \\&+\alpha e\left\{{\begin{aligned}2\mathrm {G} &\cos(\ \ n\ t+\theta )\\+\left(\sideset {^{1}}{}{\mathrm {G} }+\sideset {^{1}}{}{\mathrm {F} }\right)&\cos(\ \ n't\qquad \ \ \ +\ \ \mathrm {B} +\theta )\\+\left(\sideset {^{1}}{}{\mathrm {G} }-\sideset {^{1}}{}{\mathrm {F} }\right)&\cos(\ \ n't-2nt+\ \ \mathrm {B} -\theta )\\+\left(\sideset {^{2}}{}{\mathrm {G} }+\sideset {^{2}}{}{\mathrm {F} }\right)&\cos(2n't-\ \ nt+2\mathrm {B} +\theta )\\+\left(\sideset {^{2}}{}{\mathrm {G} }-\sideset {^{2}}{}{\mathrm {F} }\right)&\cos(2n't-3nt+2\mathrm {B} -\theta )\\+\ \ \ldots \ldots \ldots &\ldots \ldots \ldots \ldots \ldots \ldots \ldots \end{aligned}}\right\}\\&-\alpha e'\left\{{\begin{aligned}2\mathrm {H} &\cos(\ \ n't+\theta ')\\+\left(\sideset {^{1}}{}{\mathrm {H} }+\sideset {^{1}}{}{\mathrm {F} }\right)&\cos(2n't-\ \ nt+\ \ \mathrm {B} +\theta ')\\+\left(\sideset {^{1}}{}{\mathrm {H} }-\sideset {^{1}}{}{\mathrm {F} }\right)&\cos(\ \ n't-\ \qquad \quad \mathrm {B} +\theta ')\\+\left(\sideset {^{2}}{}{\mathrm {H} }+\sideset {^{2}}{}{\mathrm {F} }\right)&\cos(3n't-2nt+2\mathrm {B} +\theta ')\\+\left(\sideset {^{2}}{}{\mathrm {H} }-\sideset {^{2}}{}{\mathrm {F} }\right)&\cos(\ \ n't-2nt+2\mathrm {B} -\theta ')\\+\ \ \ldots \ldots \ldots &\ldots \ldots \ldots \ldots \ldots \ldots \ldots \end{aligned}}\right\}\\\end{aligned}}}
![{\displaystyle {\begin{aligned}&{\frac {\left(i^{2}-2\right)}{2\left(1+i^{2}\right)}}(b\ )+{\frac {i\left(i^{2}-1\right)}{\left(1+i^{2}\right)^{2}}}\left({\frac {db}{dq}}\right)+{\frac {3i}{2\left(1+i^{2}\right)}}\\&\qquad \times \left({\frac {b_{1}}{2}}\right)-{\frac {i^{2}\left(i^{2}-1\right)}{\left(1+i^{2}\right)^{2}}}\left({\frac {db_{1}}{2dq}}\right)=\mathrm {G} ,\\&{\frac {\left(i^{2}-2\right)}{2\left(1+i^{2}\right)}}(b_{1})+{\frac {i\left(i^{2}-1\right)}{\left(1+i^{2}\right)^{2}}}\left({\frac {db_{1}}{dq}}\right)+{\frac {3i}{2\left(1+i^{2}\right)}}\\&\qquad \times \left[\quad (b\ )+{\frac {1}{2}}(b_{2})\right]-{\frac {i^{2}\left(i^{2}-1\right)}{\left(1+i^{2}\right)^{2}}}\left[\quad {\frac {db}{dq}}\ +{\frac {1}{2}}\left({\frac {db_{2}}{dq}}\right)\right]=\sideset {^{1}}{}{\mathrm {G} },\\&{\frac {\left(i^{2}-2\right)}{2\left(1+i^{2}\right)}}(b_{2})+{\frac {i\left(i^{2}-1\right)}{\left(1+i^{2}\right)^{2}}}\left({\frac {db_{2}}{dq}}\right)+{\frac {3i}{2\left(1+i^{2}\right)}}\\&\qquad \times \left[{\frac {1}{2}}(b_{1})+{\frac {1}{2}}(b_{3})\right]-{\frac {i^{2}\left(i^{2}-1\right)}{\left(1+i^{2}\right)^{2}}}\left[{\frac {1}{2}}{\frac {db_{1}}{dq}}+{\frac {1}{2}}\left({\frac {db_{3}}{dq}}\right)\right]=\sideset {^{2}}{}{\mathrm {G} },\\&\ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \,;\\\\&{\frac {3i^{2}}{2\left(1+i^{2}\right)}}(b\ )+{\frac {i\left(i^{2}-1\right)}{\left(1+i^{2}\right)^{2}}}\left({\frac {db}{dq}}\right)+{\frac {i\left(1-2i^{2}\right)}{2\left(1+i^{2}\right)}}\\&\qquad \times \left({\frac {b_{1}}{2}}\right)-{\frac {i^{2}\left(i^{2}-1\right)}{\left(1+i^{2}\right)^{2}}}\left({\frac {db_{1}}{2dq}}\right)=\mathrm {H} ,\\&{\frac {3i^{2}}{2\left(1+i^{2}\right)}}(b_{1})+{\frac {i\left(i^{2}-1\right)}{\left(1+i^{2}\right)^{2}}}\left({\frac {db_{1}}{dq}}\right)+{\frac {i\left(1-2i^{2}\right)}{2\left(1+i^{2}\right)}}\\&\qquad \times \left[\quad (b)\ +{\frac {1}{2}}(b_{2})\right]-{\frac {i^{2}\left(i^{2}-1\right)}{\left(1+i^{2}\right)^{2}}}\left[\quad {\frac {db}{dq}}\ +{\frac {1}{2}}\left({\frac {db_{2}}{dq}}\right)\right]=\sideset {^{1}}{}{\mathrm {H} },\\&{\frac {3i^{2}}{2\left(1+i^{2}\right)}}(b_{2})+{\frac {i\left(i^{2}-1\right)}{\left(1+i^{2}\right)^{2}}}\left({\frac {db_{2}}{dq}}\right)+{\frac {i\left(1-2i^{2}\right)}{2\left(1+i^{2}\right)}}\\&\qquad \times \left[{\frac {1}{2}}(b_{1})+{\frac {1}{2}}(b_{3})\right]-{\frac {i^{2}\left(i^{2}-1\right)}{\left(1+i^{2}\right)^{2}}}\left[{\frac {1}{2}}{\frac {db_{1}}{dq}}+{\frac {1}{2}}\left({\frac {db_{3}}{dq}}\right)\right]=\sideset {^{2}}{}{\mathrm {H} },\\&\ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \,;\end{aligned}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/df012552b46f52735d27190dd095317cedc32dbe)
![{\displaystyle {\frac {a^{2}\left[r-r'\cos(\varphi '-\varphi )\right]}{\sideset {^{1}}{^{3}}v}}=}](https://wikimedia.org/api/rest_v1/media/math/render/svg/a5c2aad5d062cd0696a33ec397f6ab69db8e0580)
