Non-holonomic systems with symmetry allowing a conformally symplectic reduction

Non-holonomic mechanical systems can be described by a degenerate almost-Poisson structure [10] (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. [4][9]).