= Rapidly rotating saddle confinement
{title2=$\omega_{\rm slow}\simeq\omega^2/(2|\Omega|)$}
In rapid rotation, both rotating-frame modes are nearly circular and counter-rotate relative to the axes at <frequency> near $|\Omega|$. Transforming back to the laboratory leaves a slow nearly harmonic oscillation and small rapid micromotion. For positive rotation the slow ellipse also has higher-order prograde precession at rate $\omega^4/(8\Omega^3)$. These follow by expanding $\sqrt{\Omega^2\pm\omega^2}$ and combining the two laboratory circular components.<Rotating saddle trap as Foucault's pendulum by Oleg N. Kirillov and Mark Levi>[preprint pp. 2 and 6–7, model distinction and equations (12)–(18)]{ref}
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