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On the geometry of generalized Chaplygin systems

F. Cantrijn·J. Cortes·M. de Leon·D. Martin de Diego
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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.

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F. Cantrijn, J. Cortes, M. de Leon, D. Martin de Diego. 2000-11-16. On the geometry of generalized Chaplygin systems. https://arxiv.org/abs/math/0008141

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