Avoiding Zeno´s paradox in impulse-based rigid body simulation

Treating “resting” contacts (i.e., contacts with zero normal relative velocity), using forces is problematic due to inconsistent configurations. For this reason, treating resting contacts with impulses instead of forces has become common, but this approach also suffers from a significant problem: applying impulses at the time-of-contact can keep the simulation from advancing. This scenario is analogous to one of the paradoxes devised by the philosopher Zeno, and has been referred to as a Zeno point in the simulation community. I describe how to avoid Zeno points without violating the theoretical dynamic behavior of the simulated bodies and without permitting interpenetration. Two experiments demonstrate that the method works as desired where alternative approaches that required accepting interpenetration or longer running times were previously required.