Epicyclic ellipse
= Epicyclic ellipse
{title2=$X/Y=\kappa/(2\Omega)$}
In a Cartesian frame rotating with an <epicyclic guiding center>, a small planar oscillation obeys $x=X\cos(\kappa t+\chi)$ and $y=-(2\Omega X/\kappa)\sin(\kappa t+\chi)$. The ellipse is elongated azimuthally when the <radial epicyclic frequency> satisfies $\kappa<2\Omega$. <Conservation of angular momentum> makes the motion around the guiding centre retrograde.