= Translating harmonic trap on a circular orbit
{title2=$\ddot{\mathbf q}+\omega^2\mathbf q=R\Omega^2(\cos\Omega t,\sin\Omega t)$}
A nonrotating frame whose origin travels on a circle carries a spatially uniform fictitious force. A harmonic trap fixed to that origin therefore drives its relative coordinate by the displayed equation. Away from resonance its circular particular response has radius $R\Omega^2/(\omega^2-\Omega^2)$. At $\omega^2=\Omega^2\ne0$, the response grows linearly in time. Rotating the coordinate axes adds Coriolis and centrifugal terms but does not change this physical resonance condition.
Back to article page
