= Rolling constraint inside a moving circular track
{title2=$r\dot\psi=R\dot\theta-(R-r)\dot\phi$}
A circular body of radius $r$ rolls inside a circular track of radius $R$. Let $\theta$ be the track's material <rotation>, $\phi$ the absolute angle of the line joining the two centres, and $\psi$ the inner body's absolute spin angle, all with one consistent orientation. Equating contact-point velocities gives the displayed constraint. <Translation> of the track's centre cancels from that equality. A stationary track gives $\dot\psi=-(R-r)\dot\phi/r$.
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