Chaplygin systems associated to Cartan decompositions of semi-simple Lie algebras

We relate a Chaplygin type system to a Cartan decomposition of a real semi-simple Lie group. The resulting system is described in terms of the structure theory associated to the Cartan decomposition. It is shown to possess a preserved measure and when internal symmetries are present these are factored out via a process called truncation. Furthermore, a criterion for Hamiltonizability of the system on the so-called ultimate reduced level is given. As important special cases we find the Chaplygin ball rolling on a table and the rubber ball rolling over another ball.