ON DISCONTINUOUS MOTIONS IN SYSTEMS WITH UNILATERAL CONSTRAINTS

Mechanical systems with a finite number of degrees of freedom, subject to one or more unilateral geometric constraints, are considered. Apar t from the main forms of motion-flying, supported motion and non-degen erate collisions-such systems also show more complex, discontinuous mo tions, including infinitely many impacts in any neighbourhood of the s tarting time. These motions are possible not only when no continuous m otions exist, but also together with continuous motions [1]. It is pro ved that, in the case of ideal constraints, if the reactions of the co nstraints at the starting time are non-zero, there cannot be any disco ntinuous motion. In systems with dry friction there is yet another typ e of discontinuity, namely, tangential impact at zero approach velocit y. Sufficient conditions for continuity of the motion are derived for this case also. The conditions are verified with examples that use the usual models of impact. (C) 1998 Elsevier Science Ltd. All rights res erved.