9 Rotational Dynamics

Abstract This chapter studies in detail the natural motion of rigid bodies under impressed external forces and torques. The dynamical theorems of collective motion will be extended here by use of the rotation operators. The following sections discuss concepts such as the inertia operator and the spin, the inertia dyadic, and the kinetic energy of a rigid body. Any rigid body will have a system of principal axes. If necessary, three arbitrary body-fixed axes can be chosen, the inertia matrix can be calculated, and then the principal axis eigenvectors can be determined. In many situations of interest, however, the directions of the principal axes can be guessed with relative certainty from the symmetry of the rigid body. A number of rules that can be used are presented here.