Abstract
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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