LR and L+R Systems

Details LR and L+R Systems LR and L+R Systems

2009-02-10

arxiv.org/abs/0902.1656v1

J. Phys. A 42 (2009), no. 22, 225202, 18 pp

Physics

Mathematical Physics

18 pages, 1 figure

Scientific paper

We consider coupled nonholonomic LR systems on the product of Lie groups. As examples, we study $n$-dimensional variants of the spherical support system and the rubber Chaplygin sphere. For a special choice of the inertia operator, it is proved that the rubber Chaplygin sphere, after reduction and a time reparametrization becomes an integrable Hamiltonian system on the $(n-1)$--dimensional sphere. Also, we showed that an arbitrary L+R system introduced by Fedorov can be seen as a reduced system of an appropriate coupled LR system.

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