Simulation of Hard Contacts with Friction: An Iterative Projection Method

An algorithm for the simulation of mechanical systems with hard contacts and Coulomb friction is presented. The contact laws together with the switching rules between the different states of the contacts are formulated as normal cone inclusions and then generalized to contact-impact laws. By using proximal point methods, the combined contact-impact laws are rewritten as nonlinear equations and then iteratively solved within an implicit time integration algorithm. As illustrative examples, a funnel-deflector arrangement with 3,500 rigid balls and a bobsled simulator software is briefly presented. The theoretical setting is in accordance with classical Lagrangian mechanics and can be used to model various set-valued interaction laws in arbitrary finite-dimensional multibody systems.