Near-simultaneous impacts

This work considers a three-mass collision model with compliant contacts. If the masses are initially separated by a sufficient distance, the collision sequence is pairwise, that is, comprised of a series of pairwise impacts. The final velocities of each mass are then independent of the specific initial spacing. In contrast, if the initial spacing between the masses is small the three masses interact simultaneously and the final velocity state depends not only on the initial velocities, but also on the initial configuration of the system. Given the impact duration and coefficient of restitution for a pairwise collision, which can be determined from appropriate differential collision models, a two-dimensional map is derived to describe those initial conditions that lead to pairwise sequences in the three mass system. Finally, for a specific nonlinear compliance model the variation in the final velocities are characterized in terms of the initial configuration of the system.