  This paper addresses the problem of the Chaplygin ball rolling on a
horizontal plane which rotates with constant angular velocity. In this case,
the equations of motion admit area integrals, an integral of squared angular
momentum and the Jacobi integral, which is a generalization of the energy
integral, and possess an invariant measure. After reduction the problem reduces
to investigating a three-dimensional Poincare map that preserves phase volume
(with density defined by the invariant measure). We show that in the general
case the system's dynamics is chaotic.
