Quasi-Chaplygin Systems and Nonholonimic Rigid Body Dynamics

TL;DR

This paper demonstrates that the Suslov nonholonomic rigid body problem can be viewed as a generalized Chaplygin system, providing new insights into its Hamiltonian reduction and invariant manifold structure.

Contribution

It introduces a novel perspective by relating the Suslov problem to generalized Chaplygin systems, expanding the class of nonholonomic systems reducible to Hamiltonian form.

Findings

Suslov problem is almost everywhere a generalized Chaplygin system

Provides a new example of multidimensional nonholonomic system reducible to Hamiltonian form

Invariant manifolds are not necessarily tori in these systems

Abstract

We show that the Suslov nonholonomic rigid body problem can be regarded almost everywhere as a generalized Chaplygin system. Furthermore, this provides a new example of a multidimensional nonholonomic system which can be reduced to a Hamiltonian form by means of Chaplygin reducing multiplier. Since we deal with Chaplygin systems in the local sense, the invariant manifolds of the integrable examples are not necessary tori.