On almost-Poisson structures in nonholonomic mechanics

Abstract

In this paper we intend to unify different approaches to the construction of an 'almost-Poisson' bracket for mechanical systems with nonholonomic constraints. This almost-Poisson structure is subsequently used to describe the phase-space dynamics of a nonholonomic system. It is shown that when dealing with 'nonhomogeneous' constraints, the Hamiltonian equations of motion cannot be expressed in terms of the almost-Poisson bracket alone. This fact is illustrated in the case of mechanical systems with affine constraints. The problem of a rolling ball on a rotating table is treated as an example. © 1999 IOP Publishing Ltd and LMS Publishing Ltd