Inconsistencies in Modeling Impact with Friction by Algebraic Equations

This paper is concerned with inconsistent results that can be obtained when modeling rigid body collisions via algebraic equations. Newton’s approach is kinematic and fails in several cases. Poisson’s formulation has been shown lead to energetic inconsistencies, particularly in work done by the impulsive forces. This paper shows that the energetic formulation may lead to unexpected results in the magnitudes of the impulsive forces. These inconsistencies are due to the simplifying assumptions made to model collisions as occurring instantaneously. The inconsistencies increase as friction in the system becomes higher. We propose an optimization procedure for solving the algebraic equations of impact so that inconsistencies are minimized. Using experimental results, we present a discussion about the coefficients of restitution and friction.