On the Routh sphere problem

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.

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References in corpus (1)

• Poisson structures for reduced non-holonomic systems

Cited by in corpus (5)

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• Hamiltonization of solids of revolution through reduction
• Topological monodromy as an obstruction to Hamiltonization of nonholonomic systems: pro or contra?
• On the Lie integrability theorem for the Chaplygin ball
• Nonholonomic Noetherian symmetries and integrals of the Routh sphere and Chaplygin ball