On the geometry of generalized Chaplygin systems
Abstract
Some aspects of the geometry and the dynamics of generalized Chaplygin systems are investigated. First, two different but complementary approaches to the construction of the reduced dynamics are reviewed: a symplectic approach and an approach based on the theory of affine connections. Both are mutually compared and further completed. Next, a necessary and sufficient condition is derived for the existence of an invariant measure for the reduced dynamics of generalized Chaplygin systems of mechanical type. A simple example is then constructed of a generalized Chaplygin system which does not verify this condition, thereby answering in the negative a question raised by Koiller.
Cite
@article{arxiv.math/0008141,
title = {On the geometry of generalized Chaplygin systems},
author = {F. Cantrijn and J. Cortes and M. de Leon and D. Martin de Diego},
journal= {arXiv preprint arXiv:math/0008141},
year = {2007}
}
Comments
33 pages, no figures; added references for Section 4. To appear in Math. Proc. Cambridge Philos. Soc