Vibro-Impact Problems with Dry Friction---Part II: Tangential Contacts and Frictional Catastrophes

Abstract

As in part I [SIAM J. Math. Anal., 47 (2015), pp. 3285--3313] we consider a discrete mechanical system with a nontrivial inertia operator subjected to unilateral constraints with dry friction. We focus on the behavior of the system in case of tangential contact. Then frictional catastrophes, i.e., velocity jumps without collision, may occur, leading to the famous Painleve's paradoxes. By a precise study of the approximate trajectories constructed in part I in a neighborhood of this kind of events, we show that the problem admits a solution which encompasses such phenomena.