Contact and Impact

Abstract

When two rigid bodies come into contact, they become subject to a contact constraint which says that the two bodies are not allowed to penetrate. If φ is a measure of the signed distance between them, meaning that φ < 0 if they overlap, then the contact constraint is given by the inequality φ ≥ 0. The forces that impose this constraint are similarly one-sided: they can act to prevent penetration, but not to prevent separation—they can repel, but not attract. If two bodies meet with velocities that are not consistent with the contact constraint between them, then an impulse is generated that causes a step change in their velocities. We call this event an impact.