TABLE OF CONTENTS This chapter contains results on the three-dimensional kinematics of rigid bodies. We discuss several useful classical representations for the velocity and acceleration vectors of any material point of a rigid body. We also discuss the angular velocity vector ?, the linear momentum G, angular momenta H , H O, and H A, and kinetic energy T of rigid bodies and the inertias that accompany them. The chapter concludes with a discussion of the configuration manifold for a rigid body.
The origin of most of the material in this chapter can be traced to Euler s seminal work on rigid body dynamics in the 1750s. Since that time, his theory has been used to develop models for a wide range of mechanical systems and various treatments of his work have appeared. Recently, a tensor-based notation has been used by Beatty [15], Casey [26, 28], Fox [65], Greenwood [80], and Gurtin [84]. In this book, we follow their work as it leads to transparent developments particularly with regards to inertias and angular velocities.
To discuss the kinematics of rigid bodies, it is convenient to follow some developments in continuum mechanics and define the reference and present configuration of a rigid body. First, a body 
is considered to be a collection of material points (mass particles or particles). We denote a material point of by X. The position of the material point X, relative to a...
