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.
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