Title: Time-stepping methods for rigid-body dynamics with contact and friction.

The simulation of the dynamical behavior of a system with multiple bodies subject to joint, non-interpenetration and frictional constraints is a fundamental endeavor for several applications including robotics and virtual reality. An important obstacle, however, in the development of this field has been the Painleve type inconsistency of the Coulomb model: certain configurations will not have a classical (acceleration-force) solution when friction is present. Here we present a velocity-impulse time-stepping scheme that is guaranteed to have a solution for any configuration and friction coefficient. At each step the scheme solves a potentially nonconvex linear complementarity problem with a copositive matrix. We also show how the scheme can modified to accommodate the most commonly encountered stiff forces. The stability of the scheme is demonstrated by several examples.