On the Routh sphere problem

TL;DR

This paper explores the embedding of the nonholonomic Routh sphere problem into a Hamiltonian framework, revealing a connection between nonholonomic and Hamiltonian systems through Poisson structures.

Contribution

It introduces a novel embedding of the Routh sphere's vector field into a subgroup of commuting Hamiltonian vector fields, linking nonholonomic and Hamiltonian dynamics.

Findings

Embedding of the Routh sphere into Hamiltonian vector fields

Reduction of Poisson brackets to canonical form on e(3)

Establishment of a relation between nonholonomic and Hamiltonian systems

Abstract

We discuss an embedding of a vector field for the nonholonomic Routh sphere into a subgroup of commuting Hamiltonian vector fields on six dimensional phase space. The corresponding Poisson brackets are reduced to the canonical Poisson brackets on the Lie algebra e(3). It allows us to relate nonholonomic Routh system with the Hamiltonian system on cotangent bundle to the sphere with canonical Poisson structure.