On the Poisson structures for the Chaplygin ball and its generalizations

Construction of the Poisson structures for the nonholonomic Chaplygin and Borisov–Mamaev–Fedorov systems is discussed. The corresponding vector fields are conformally Hamiltonian and generalized conformally Hamiltonian vector fields with respect to the linear in momenta Poisson brackets. We suppose that this difference is closely related with the non-trivial deformation of canonical Poisson bivector, which appears in the Borisov–Mamaev–Fedorov case.