Solution to indeterminate multipoint impact with frictional contact using constraints

This work presents a method for determining the post-impact behavior of a rigid body undergoing multiple, simultaneous impact 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 is examined. Velocity constraints are 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 impact point is then determined and appropriate methods are used to resolve the post-impact velocities. These techniques are applied to a 3-D model of a ball which is forced to impact a corner between the ground and two wall planes. Additionally, a rocking block example is considered. Simulations are presented for 2-D and 3-D cases of the ball example, and a 2-D model of the rocking block problem to demonstrate the effectiveness of the proposed approach.