Acceleration Analysis of Rigid-Body Motions

The concept of angular acceleration of a rigid-body motion is introduced in this chapter. Moreover, the relationships between the angular acceleration of the rigid body and the time derivatives of the associated rotational invariants are derived, while the acceleration field of the body is derived in terms of the angular-acceleration tensor. Unlike the displacement and the velocity fields, the acceleration field, in general, contains one point of zero acceleration that is unique. Indeed, as shown in this chapter, the angular-acceleration tensor is, in general, nonsingular, and becomes singular only in the particular case in which the body instantaneously undergoes a rotation about a stationary axis. Thus, in the case of acceleration fields, no theorem similar to that of Chasles’ for displacement fields, or its counterpart for velocity fields, exists.