 Solution

A holonomic constraint can be expressed as $f(q_1,\dots ,q_n,t)=0$, rather than as a genuinely nonintegrable relation among velocities. A fixed rod length is an example. Rolling along a single straight incline also gives an integrable relation $s+R\theta =\text{constant}$ with the sign convention used below; arbitrary rolling in more dimensions need not be holonomic.