= Oblate-quadrupole epicyclic precession
{title2=$\kappa^2=n^2(1-3\alpha^2/R^2),\quad\nu^2=n^2(1+9\alpha^2/R^2)$}
For $\Phi=-\mu/r+\alpha^2\mu(3z^2-r^2)/r^5$, a nearly circular equatorial orbit has $n^2=\mu/R^3$ and azimuthal frequency $\Omega_c^2=n^2(1+3\alpha^2/R^2)$. The <radial epicyclic frequency> is $\kappa^2=R\,d\Omega_c^2/dR+4\Omega_c^2$, and the <vertical epicyclic frequency> is $\nu^2=\partial_z^2\Phi|_{z=0}$. Radial stability requires $R^2>3\alpha^2$. The <nodal precession> rate $\Omega_c-\nu$ is negative and the <apsidal precession> rate $\Omega_c-\kappa$ positive. These sign statements concern small eccentricity and inclination. For an arbitrary inclined orbit, the averaged <argument of periapsis> instead evolves as $(3/2)n\alpha^2[5\cos^2i-1]/[a^2(1-e^2)^2]$ and can regress.
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