Rigid Body Dynamics

The motion of a rigid body contains two parts: linear motion and angular motion. In this document, we will study both motions. We will also discuss how to detect collisions and estimate collision responses. To simplify our notations, we will follow the standard formats: bold fonts are vectors, italic fonts are scalars, and UPPERCASES are matrices. The physics quantities associated with linear motion are: position, velocity, force, ... The physics quantities associated with angular motion are: orientation, angular velocity, torque, ...