  We derive an optimal control formulation for a nonholonomic mechanical system
using the nonholonomic constraint itself as the control. We focus on Suslov's
problem, which is defined as the motion of a rigid body with a vanishing
projection of the body frame angular velocity on a given direction
$\boldsymbol{\xi}$. We derive the optimal control formulation, first for an
arbitrary group, and then in the classical realization of Suslov's problem for
the rotation group $SO(3)$. We show that it is possible to control the system
using the constraint $\boldsymbol{\xi}(t)$ and demonstrate numerical examples
in which the system tracks quite complex trajectories such as a spiral.
