Nonholonomic systems with symmetry allowing a conformally symplectic reduction
arXiv:math-ph/0203013 · doi:10.1007/978-1-4419-9058-7_15
Abstract
Non-holonomic mechanical systems can be described by a degenerate almost-Poisson structure (dropping the Jacobi identity) in the constrained space. If enough symmetries transversal to the constraints are present, the system reduces to a nondegenerate almost-Poisson structure on a ``compressed'' space. Here we show, in the simplest non-holonomic systems, that in favorable circumnstances the compressed system is conformally symplectic, although the ``non-compressed'' constrained system never admits a Jacobi structure (in the sense of Marle et al.).
8 pages. A slight edition of the version to appear in Proceedings of HAMSYS 2001