Algebraic Solution To The Planar Rigid Body Impact Problem

Abstract

For systems of rigid bodies that undergo impacts, a series of closed-form equations are developed to solve for post-impact velocities which simulate a real-world (energy-consistent) interaction. The analysis is based in the impulse domain, and requires that the surface interaction be characterizable by Coulomb friction and an energetic coefficient of restitution. No iteration, optimization, or numerical methods are used.