Coordinate-Free Representation of Rotational Motions

摘要

The rotation of a rigid body may be represented by a unit axis and the angle ofrotation about that axis. Here we investigate the representation in this form of the rotation equivalent to two successive rotations, and derive equations of motion of the body in terms of its angular velocity. The relationship of our results to those of the quantum theory of angular momentum is also discussed with particular reference to the Baker-Campbell-Hausdorff expansion.