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

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. (C) 2010 Elsevier B.V. All rights reserved.


Published in:
Differential Geometry And Its Applications, 28, 436-453
Year:
2010
Publisher:
Elsevier
ISSN:
0926-2245
Keywords:
Laboratories:




 Record created 2011-12-16, last modified 2018-01-28


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