LR and L+R systems

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.