Collision-free motion in systems with non-retaining constraints

The properties of collision-free periodic motions in a system with a non-retaining constraint are studied. In motions of this kind the intervals in which the constraint is in a strained or slackened state alternate, and moreover the transition of the constraint to a strained state does not involve collisions. Conditions are derived for the existence of collision-free motions, and their relationship to singularities of differentiable mappings is ascertained. The ``attracting'' properties of collision-free motions are established: under certain conditions they are analogous to semistable limit cycles. The results are illustrated by examples: a body on an elastic leg [1] and a link-up of bodies in a satellite orbit [2].