# American Institute of Mathematical Sciences

September  2014, 6(3): 417-440. doi: 10.3934/jgm.2014.6.417

## Poisson structures for two nonholonomic systems with partially reduced symmetries

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

Received  January 2013 Revised  May 2014 Published  September 2014

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.
Citation: Andrey Tsiganov. Poisson structures for two nonholonomic systems with partially reduced symmetries. Journal of Geometric Mechanics, 2014, 6 (3) : 417-440. doi: 10.3934/jgm.2014.6.417
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