Several areas of intense recent interest, such as robotics and virtual reality, depend on the efficient simulation of several objects subject to non interpenetration and Coulomb friction constraints. Unfortunately, even for very simple examples it can be shown that the classical acceleration-force approach will fail to produce a solution that is needed to advance the simulation in time.
We present a time-stepping scheme, based on a linear complementarity approach that is guaranteed to produce a physically meaningful solution at every step. We also show that a variation of the scheme can accomodate very stiff forces, the kind of which can be expected to appear in realistic simulations. Several simulations with contact, collision and friction will be presented to illustrate the behavior of the method.