Classifying dynamic behavior during three dimensional frictional rigid body impact

Abstract

We model and analyze three dimensional rigid body impact with Coulomb friction and Poisson restitution. The differential equations that describe the progress and outcome of the impact induce a flow in the tangent velocity space which defines the qualitatively different sliding behavior that can occur. We show that the flow patterns depend only on the inertial parameters at the point of contact. We associate each of the possible flow patterns with a distinct region in a three dimensional parameter space. By examining the mass parameters and the initial conditions, we can determine the corresponding flow pattern and the possible outcomes of the impact. The equations of motion cannot be solved in a closed form, but by analyzing the flow at the point of sticking, we can avoid instabilities in the numerical integration of the equations.