Approximate Force History Estimation in Multi-Point Non-Smooth Collisions

Collisions between hard objects cause abrupt changes in the velocities of the system, which are characterized by very large contact forces over very small time-durations. A common approach in the analysis of such collisions is to describe the system velocities using an impulse-momentum based relationship. The time-duration of impact and the deformations at the contact points are usually assumed to be negligible in such impact models, and the system velocities are evolved in terms of the impulses on the system. This type of impact models are usually relevant for hard (rigid) impacts, where deformations at the contact points can be considered negligible. However, these models cannot determine the forces during the impact process. The main objective of this work is to reformulate the impulse-momentum based model to determine the forces during an impact event, by relaxing the rigidity assumption to allow small deformations at the contact points.