= Orbit volume in an axisymmetric Stäckel potential
{title2=$p_\tau^2\geq0$}
For fixed $E,l,I$, separated motion obeys $p_\tau^2=[E\tau+G(\tau)-I+(\alpha-\beta)l^2/(2(\tau+\alpha))]/[2(\tau+\alpha)(\tau+\beta)]$. Allowed intervals are where this is nonnegative, with turning points and coordinate-fold endpoints treated separately. A generic nonresonant bound <orbit> with $l\ne0$ circulates azimuthally and densely samples a projected <volume> bounded by confocal spheroids and hyperboloids. It is not uniformly distributed in <volume>. Resonant or zero-angular-momentum <orbits> can project to lower-dimensional regions; integrability alone does not imply that every <orbit> fills a three-dimensional shell.
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