Generalizations of classical integrable nonholonomic rigid body systems

Nonholonomic systems with an invariant measure: the Suslov, Chaplygin and V eselov-Veselova problem are considered. New families of integrable potentia l perturbations of these non-Hamiltonian systems are constructed. We also o btain a similar result for a classical Hamiltonian system of the motion of a rigid body fixed at a point.