Nonholonomic stability aspects of piecewise holonomic systems

We consider mechanical systems with intermittent contact that are smooth an d holonomic except at the instants of transition. Overall such systems can be nonholonomic in that the accessible configuration space can have larger dimension than the instantaneous motions allowed by the constraints. The kn own examples of such mechanical systems are also dissipative. By virtue of their nonholonomy and of their dissipation such systems are not Hamiltonian . Thus there is no reason to expect them to adhere to the Hamiltonian prope rty that exponential stability of steady motions is impossible. Since nonho lonomy and energy dissipation are simultaneously present in these systems, it is usually not clear whether their sometimes-observed exponential stabil ity should be attributed solely to dissipation, to nonholonomy, or to both. However, it is shown here on the basis of one simple example, that the obs erved exponential stability of such systems can follow solely from the nonh olonomic nature of intermittent contact and not from dissipation. In partic ular, it is shown that a discrete sister model of the Chaplygin sleigh, a r igid body on the plane constrained by one skate, inherits the stability eig envalues of the smooth system even as the dissipation tends to zero. Thus i t seems that discrete nonholonomy can contribute to exponential stability o f mechanical systems.