Simultaneous oblique impacts and contacts in multibody systems with friction

This paper presents a new dissipation principle for resolving post-impact tangential velocities after simultaneous oblique impact events on a system composed of interconnected rigid bodies. In this work, contact is considered as a succession of impacts so that simultaneous contacts and impacts can be treated using the same framework. This treatment includes Coulomb friction and considers hard impacts where deformation of the impacting surfaces is negligible. The impact problem is addressed using the complementarity conditions which lead to an investigation of the relationship between post-impact velocities and feasible coefficients of friction. These conditions do not define a unique post-impact velocity so a dissipation principle is proposed which is encoded as an optimization problem. This solution preserves the discontinuity between the static and dynamic coefficients of friction. The approach is illustrated by simulation of a planar bicycle-like structure with elliptical wheels.