Planar collision-type dependence on incident angle and on friction coefficient

Abstract

This work addresses the ‘hard collision’ approach to the solution of planar, simple non-holonomic systems undergoing a one-point collision-with-friction problem, showing that (i) there are no coherent types of collision whereby forward sliding follows sticking, unless the initial relative tangential velocity of the colliding points vanishes; and (ii) the type of collision can be determined directly, given the collision angle of incidence \(\alpha\) and Coulomb’s coefficient of friction \(\mu\) between the colliding points. The classic hitting rod problem is used to illustrate the \(\alpha \)–\(\mu\) collision-type dependence. Finally, the relation between collision with friction and tangential impact problems in multibody systems is briefly discussed.