Existence and uniqueness of the motion of a particle subject to a unilateral constraint and friction

Abstract

We prove that there exists a unique solution to the initial value problem describing the motion of a particle subject to a unilateral constraint and Coulomb friction, if the external force acting on the particle is an analytic function of time and of the particle’s position and velocity. Previous work claimed that this problem has a local series solution that corresponds to an analytic function, after any impacts have been resolved. However, a counterexample to that claim was recently discovered, involving a particle starting to slide, in which the series solution is divergent, and thus does not correspond to an analytic function. This paper corrects previous arguments by considering a general formal series solution for a particle that is starting to slide.