Central potential

A central potential depends only on distance from a fixed centre, $V(\mathbf{x})=V(|\mathbf{x}|)$. Its force is radial, and rotational symmetry implies conservation of angular momentum.

Adding an inverse-cube force can preserve radial motion while rescaling angular motion. For potential $-A/r+B/r^2$ and angular momentum $L$, the radial effective potential equals that of $-A/r$ with effective angular momentum $\sqrt{L^2+2mB}$ when this is real.