2000/08/31 by F. Cantrijn, J. Cortes, M. de Leon +1 · 1 citation
Mathematics · Physics and Astronomy · #math.DS #math-ph #math.MP #math.SG #msc:58F05 #msc:70F25 #msc:70Hxx
published as Math. Proc. Camb. Philos. Soc. 132 (2002), 323-351 · 33 pages, no figures; added references for Section 4. To appear in Math. Proc. Cambridge Philos. Soc
arxiv created 2000/11/16 · arxiv updated 2009/11/30
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.