Frictionless multiple impacts in multibody systems. I. Theoretical framework

A new method is proposed that can deal with multi-impact problems and produce energetically consistent and unique post-impact velocities. A distributing law related to the energy dispersion is discovered by mapping the time scale into the impulsive scale for bodies composed of rate-independent materials. It indicates that the evolution of the kinetic energy during the impacts is closely associated with the relative contact stiffness and the relative potential energy stored at the contact points. This distributing law is combined with the Darboux - Keller method of taking the normal impulse as an independent ' time-like' variable, which obeys a guideline for the selection of an independent normal impulse. Local energy losses are modelled with energetic coefficients of restitution at each contact point. Theoretical developments are presented in the first part in this paper. The second part is dedicated to numerical simulations where numerous and accurate results prove the validity of the approach.