L = 1 2 μ ( r ˙ 2 + r 2 θ ˙ 2 ) + k r {\displaystyle L={\frac {1}{2}}\mu ({\dot {r}}^{2}+r^{2}{\dot {\theta }}^{2})+{\frac {k}{r}}}
방정식은 두 가지가 나오는데,
ℓ = μ r × r θ ˙ {\displaystyle \ell =\mu r\times r{\dot {\theta }}}
μ r ¨ = μ r θ ˙ 2 − k r 2 = ℓ 2 μ r 3 − k r 2 {\displaystyle \mu {\ddot {r}}=\mu r{\dot {\theta }}^{2}-{\frac {k}{r^{2}}}={\frac {\ell ^{2}}{\mu r^{3}}}-{\frac {k}{r^{2}}}}
Orbit equation은 d 2 u d θ 2 + u = μ k / ℓ 2 {\displaystyle {\frac {d^{2}u}{d\theta ^{2}}}+u=\mu k/\ell ^{2}}
