Two integrable models of rolling balls over a sphere

Abstract

In this talk we consider the nonholonomic problem of rolling without slipping and twisting of a n-dimensional ball over a fixed (n−1)-dimensional sphere. This is a SO(n)-Chaplygin system with an invariant measure that reduces to the tangent bundle TSn−1. We describe two classes of inertia operators, such that corresponding systems are integrable. In the first class we use the Chaplygin reducing multiplier method, while in the second class we obtain integrability directly — without Hamiltonization.