Rigid body mechanics provides a popular and convenient way of modeling many mechanical systems of the real world. When two nominally rigid bodies collide, the collision contact forces are determined by deformations in these bodies. This happens in a way that remains important in the limit of high stiffness and small during-collision displacements. Two balls made of different materials, when dropped from the same moderate height and on to the same ground, can rebound to different extents. These rebounds cannot be predicted from within rigid body mechanics without additional constitutive modeling assumptions, the most famous of them being the coefficient of restitution. These constitutive assumptions or collision laws are mathematical rules that allow us to approximately describe the collision within the world of rigid body mechanics. The dynamics model for the system uses these rules to jump across the short and violent collisional interaction, on to, say, another phase of well-defined smooth motions. To emphasize the difference between collisional and smooth motions, imagine that these two same balls rest on the ground - the normal reaction is now determined by the weight of the balls alone, and can be predicted within rigid body mechanics without additional constitutive assumptions.

The papers below address various issues in modeling collisions within the rigid body dynamics framework, and present a simple model that has several attractive features.