Simulation Of Indeterminate Multi-point Impact And Contact With Friction

Abstract

This work presents a method for determining the post-impact behavior of a rigid-body undergoing simultaneous, multiple impacts with friction. A discrete algebraic model is used with an event-driven function which finds impact events. In this work, the indeterminate nature of the equations of motion encountered at impact are examined. A velocity constraint is developed based on the rigid-body assumption to address the equations and an impact law is used to determine the impulsive forces. The slip-state of each contact point is then determined and appropriate methods are used to resolve the post-impact velocities. Friction is treated as a complementarity problem and a set complementarity conditions are formulated using Coulomb's friction law. Additional constraints are composed in terms of a dissipation principle to yield a solution for the post-impact tangential velocities. These works will be applied to a simple planar model of a ball which is forced to impact a corner between the ground and a wall. Computer simulations will be presented to demonstrate the post-impact behavior of a rigid-body which experiences simultaneous, multiple impacts with friction.