On Newton’s and Poisson’s Rules of Percussive Dynamics

Abstract

Newton’s and Poisson ’s rules are widely used in percussive dynamics because they lead to an “all linear” solution. However, they are in general energetically inconsistent in rough collisions. The equivalence between both rules and a broad condition for them to be energetically consistent is presented for single point collisions in multibody systems with perfect constraints. It is fulfilled in collisions described by equations of motion with constant coefficients—sliding in the same direction or no sliding—and in “balanced” collisions—sliding velocity would not change if friction were negligible—Coulomb’s friction and infinite tangential stiffness are assumed at the collision point.