Stäckel potential (source code)

= Stäckel potential
{c}
{title2=$\psi=\frac{G(\lambda)-G(\mu)}{\lambda-\mu}$}

A <Stäckel potential> allows additive separation of the <Hamilton-Jacobi equation> in an orthogonal coordinate system. In axisymmetric <prolate spheroidal coordinates>, the relative-potential form is $\psi=[G(\lambda)-G(\mu)]/(\lambda-\mu)$. It gives <energy>, axial <angular momentum> and an independent third separation <integral>. Here $G$ is a one-variable generating function, not the gravitational constant. Generic bounded <orbits> are regular invariant-torus motions; resonance and coordinate degeneracy require separate treatment.