Dynamics of the Chaplygin ball on a rotating plane

Abstract

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.

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Cited by in corpus (2)

• Hamiltonization and separation of variables for Chaplygin ball on a rotating plane
• Nonholonomic Noetherian symmetries and integrals of the Routh sphere and Chaplygin ball