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. Apart from the main forms of motion—flying, supported motion and non-degenerate collisions—such systems also show more complex, discontinuous motions, including infinitely many impacts in any neighbourhood of the starting time. These motions are possible not only when no continuous motions exist, but also together with continuous motions 1]. It is proved that, in the case of ideal constraints, if the reactions of the constraints at the starting time are non-zero, there cannot be any discontinuous motion. In systems with dry friction there is yet another type of discontinuity, namely, tangential impact at zero approach velocity. 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.