ON THE IMPLEMENTATION OF NONHOLONOMIC MECHANICAL CONSTRAINTS

The problem of the implementability of mechanical constraints is treated as the problem of existence of conditions leading to the effect of the constraint [1-4]. The constraint effect can be achieved, for example, by the introduction of appropriate dissipative forces. These forces are referred to as the implementing forces. Such forces provide that the motions of the system are close to the constrained motions, i.e., the unconstrained motions converge to the constrained ones as the dissipation factor increases without limit. In the present paper, we construct the implementing forces that provide the proximity of the motions in another sense. These forces provide the stability of the motions corresponding to the constrained systems. The issue of the implementation of constraints is related to the problem of consistency of models of nonholonomic mechanical systems [1-3]. The construction of equivalent models for constrained mechanical systems opens new possibilities for solving problems of dynamics of such systems [2,4].