Rigid body collisions with friction

Abstract

An energetically consistent theory is presented for dynamics of partly elastic collisions between somewhat rough rigid bodies with friction that opposes slip. This theory is based on separately accounting for frictional and non-frictional sources of dissipation. Alternative theories derived from Newton’s impact law or Poisson’s impact hypothesis are shown to be valid only for central (collinear) or non-frictional collisions; generally the latter theories yield erroneous energy dissipation if small initial slip stops during collision between eccentric bodies. Collision processes are complex when small slip is stopped by friction; then either the direction of slip reverses or contact points roll without slip. An inconsistent theory based on Newton’s impact law can yield erroneous energy increases when slip stops during collision; the consistent theory always dissipates energy. The impact law that specifies a simple proportionality between normal components of contact velocity for incidence and rebound is not applicable in any range of incident velocities with small slip if the collision is non-collinear with friction. In Percussion the force or Impetus whereby one body is moved may cause another body against which it strikes to be put in motion, and withal lose some of its strength or swiftness. (J. Wallis, 1668)