Rolling balls over spheres in Rⁿ

Abstract

We study the rolling of the Chaplygin ball inRn over a fxed (n - 1)-dimensional sphere without slipping and without slipping and twisting. The problems can be naturally considered within a framework of appropriate modifcations of the L + R and LR systems-well known systems on Lie groups with an invariant measure. In the case of the rolling without slipping and twisting, we describe the SO(n)-Chaplygin reduction to Sn-1 and prove the Hamiltonization of the reduced system for a special inertia operator.