Stochastic chaplygin systems

We mimic the stochastic Hamiltonian reduction of Lazaro-Cami and Ortega [18, 19] for the case of certain nonholonomic systems with symmetries. Using the nonholonomic connection it is shown that the drift of the stochastically perturbed n-dimensional Chaplygin ball is a certain gradient of the density of the preserved measure of the deterministic system.