Poisson structures for two nonholonomic systems with partially reduced symmetries

Andrey Tsiganov

doi:10.3934/jgm.2014.6.417

Article Contents

2014, Volume 6, Issue 3: 417-440. Doi: 10.3934/jgm.2014.6.417

This issue Previous Article Stability of Hamiltonian relative equilibria in symmetric magnetically confined rigid bodies Next Article

Poisson structures for two nonholonomic systems with partially reduced symmetries

Andrey Tsiganov^1,

1.
Department Computational Physics, Faculty of Physics, St.Petersburg State University, Ulyanovskaya, 3, St.Petersburg 198504

Received: December 31, 2012

Revised: April 30, 2014

Published: August 2014

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Abstract

We consider nonholonomic systems which symmetry groups consist of two subgroups one of which represents rotations about the axis of symmetry. After nonholonomic reduction by another subgroup the corresponding vector fields on partially reduced phase space are linear combinations of the Hamiltonian and symmetry vector fields. The reduction of the Poisson bivectors associated with the Hamiltonian vector fields to canonical form is discussed.

Keywords:

Integrable nonholonomic systems,
Poisson geometry.

Mathematics Subject Classification: Primary: 34D20; Secondary: 70E40, 37J35.

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