Inverse-cube central orbit classification
= Inverse-cube central orbit classification
For nonzero <angular momentum> $L$, put $u=1/r$ and $\lambda=1+2mB/L^2$. The <Binet equation> is $u_{\theta\theta}+\lambda u=0$. Positive $\lambda$ gives cosine scattering branches, zero gives linear reciprocal radius, and negative gives exponential combinations, with <energy> distinguishing sinh, exponential and cosh branches. Only intervals with $u>0$ are physical.