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    • 12.3: Separation of Variables for a Central Potential; Cyclic Variables
      https://phys.libretexts.org/Bookshelves/Classical_Mechanics/Graduate_Classical_Mechanics_(Fowler)/12%3A_The_Hamilton-Jacobi_Equation/12.03%3A_Separation_of_Variables_for_a_Central_Potential_Cyclic_Variables
      \dfrac{1}{2 m}\left(\dfrac{\partial S_{0}}{\partial r}\right)^{2}+V(r)+\dfrac{1}{2 m r^{2}}\left(\dfrac{\partial S_{0}}{\partial \theta}\right)^{2}+\dfrac{1}{2 m r^{2} \sin ^{2} \theta}\left(\dfrac{\p...\dfrac{1}{2 m}\left(\dfrac{\partial S_{0}}{\partial r}\right)^{2}+V(r)+\dfrac{1}{2 m r^{2}}\left(\dfrac{\partial S_{0}}{\partial \theta}\right)^{2}+\dfrac{1}{2 m r^{2} \sin ^{2} \theta}\left(\dfrac{\partial S_{0}}{\partial \phi}\right)^{2}=E \dfrac{1}{2 m}\left(\dfrac{\partial S_{0}}{\partial r}\right)^{2}+V(r)+\dfrac{1}{2 m r^{2}}\left[\left(\dfrac{\partial S_{0}}{\partial \theta}\right)^{2}+\dfrac{p_{\phi}^{2}}{\sin ^{2} \theta}\right]=E

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