1 Rapid Collision Dynamics for Multiple Contacts with Friction

Abstract

We examine the interaction of complex two-dimensional rigid bodies with friction. Given their idealized description, many different feasible solutions for frictional contact and collision are possible. The usual assumptions of noninterpenetration and negligible deformation at the global scale constrain contact behaviors, while incomplete descriptions of material properties at the local scale allow for a large amount of latitude in solution methods. Existing techniques for the multiple contact problem with friction either depend upon collision ordering (propagation methods) or apply LCP methods. We propose a method that generalizes Moreau’s impact law to formulate a simple but complete contact law in which both multiple constraints and multiple contacts are possible. Our algorithm finds a simultaneous solution for a system of contacts. Its implementation is simple and obtains real-time speeds.