THE ENERGY-MOMENTUM METHOD FOR THE STABILITY OF NONHOLONOMIC SYSTEMS

In this paper, we analyze the stability of relative equilibria of non- holonomic systems (that is, mechanical systems with non-integrable con straints such as rolling constraints). In the absence of external diss ipation, such systems conserve energy but nonetheless can exhibit both neutrally stable and asymptotically stable, as well as linearly unsta ble relative equilibria. To carry, out the stability analysis, we use a generalization of the energy-momentum method combined with the Lyapu nov-Malkin theorem and the center manifold theorem. While this approac h is consistent with the energy-momentum method for holonomic systems, it extends it in substantial ways. The theory is illustrated with sev eral examples, including the rolling disk, the roller racer and the ra ttleback top.