Hamilton’s principle and the rolling motion of a symmetric ball

Abstract

In this paper, we show that the trajectories of a dynamical system with nonholonomic constraints can satisfy Hamilton’s principle. As the simplest illustration, we consider the problem of a homogeneous ball rolling without slipping on a plane. However, Hamilton’s principle is formulated either for a reduced system or for a system defined in an extended phase space. It is shown that the dynamics of a nonholonomic homogeneous ball can be embedded in a higher-dimensional Hamiltonian phase flow. We give two examples of such an embedding: embedding in the phase flow of a free system and embedding in the phase flow of the corresponding vakonomic system.