= Nonholonomic constraint
A <nonholonomic constraint> is a nonintegrable restriction on allowed <velocities>: it cannot locally be replaced by relations among <generalized coordinates> and time. In contrast, a velocity equation $r\dot\phi-R\dot\theta=0$ with constant radii integrates to a <holonomic constraint> $r\phi-R\theta=C$. <Rolling without slipping> is therefore not automatically nonholonomic: planar rolling on a prescribed curve can be holonomic, whereas rolling with additional directional freedoms can impose nonintegrable velocity constraints. Unwrapped angles may be needed to record the winding of a rolling trajectory.
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