TABLE OF CONTENTS In this chapter, constraints and the forces and moments that enforce them in the dynamics of rigid bodies are discussed. In particular, the constraints associated with interconnected rigid bodies, rolling rigid bodies, and sliding rigid bodies along with prescriptions for the associated constraint forces and moments are presented. We also discuss Lagrange s prescription for constraint forces and constraint moments and outline its limitations. It also proves convenient to discuss potential energies and their associated conservative forces and moments. Our discussion includes as examples springs and central gravitational fields. It has obvious parallels to the treatment of constraints and their associated forces and moments.
Constraints in the motions of rigid bodies usually arise in two manners. First, the rigid body is connected to another rigid body in such a way that its relative motion is constrained. The connections in question are usually in the form of joints. The second manner in which constraints arise occurs when one rigid body is rolling or sliding on the other. As in particles, the constraints we discuss can be classified as integrable or nonintegrable, and this classification is important in dynamics because it may lead to considerable simplification in the formulation of the equations governing the motion.
In our discussion, we consider two rigid bodies, 
and 
(see Figure 8.1). We can consider the case of a rigid body interacting with the ground by prescribing the velocity vector of the center of mass and the angular velocity vector of either...
