Chaplygin systems associated to Cartan decompositions of semi-simple Lie groups (Q980900)

A very interesting relationship between a Chaplygin type system and the Cartan decomposition of a real semi-simple Lie group is presented and so, the resulting system is described by using the structure theory associated to the Cartan decomposition. Namely, it is shown to possess a preserved measure and when internal symmetries are present these are factored out through a process called \textit{truncation}. Also, a condition for Hamiltonizability of the system on so-called \textit{ultimate reduced level} is given. The Chaplygin ball rolling on a table and the rubber ball rolling over another ball are examples in this framework.