Collisions of Constrained Rigid Body Systems with Friction

Abstract

A new approach is developed for the general collision problem of two rigid body systems with constraints (e.g., articulated systems, such as massy linkages) in which the relative tangential velocity at the point of contact and the associated friction force can change direction during the collision. This is beyond the framework of conventional methods, which can give significant and very obvious errors for this problem, and both extends and consolidates recent work. A new parameterization and theory characterize if, when and how the relative tangential velocity changes direction during contact. Elastic and dissipative phenomena and different values for static and kinetic friction coefficients are included. The method is based on the explicitly physical analysis of events at the point of contact. Using this method, Example 1 resolves (and corrects) a paradox (in the literature) of the collision of a double pendulum with the ground. The method fundamentally subsumes other recent models and the collision of rigid bodies; it yields the same results as conventional methods when they would apply (Example 2). The new method reformulates and extends recent approaches in a completely physical context.