Rotating saddle trap
= Rotating saddle trap
{title2=$|\Omega|>\omega$}
A planar quadratic saddle $m\omega^2(x^2-y^2)/2$ rotated at angular <speed> $\Omega$ becomes linearly confining for the displayed strict inequality. Its rotating-frame mode <frequencies> obey $\epsilon_\pm^2=\Omega^2\pm\omega^2$. Equality has a zero-frequency secular mode and is not robust bounded-motion stability. This is a rotating potential model; a rolling ball on an actual surface has additional constraints.