Skip to main content Contents Index Prev Up Next \(\newcommand{\val}{Val\text{00E9}ry}
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Chapter 9 Mass Distribution
In this chapter, we are still not concerned with relating the motion of mechanical systems to the causes responsible for such motion. The dynamic behavior of a rigid body depends upon the manner in which mass is distributed over its volume. We introduce the concept of mass for an arbitrary continuum. In fact, we will consider at first arbitrary (deformable) material systems for which many of the notions defined in this chapter are relevant. The standard assumption of classical mechanics is that the system’s mass remains constant. After defining the notion of center of mass , we tie the concept of mass to such kinematic quantities as the velocity and acceleration fields to define kinetic quantities, namely the linear momentum, angular momentum, dynamic moment , and kinetic energy of a material system. More specifically, we shall define two vector fields of kinetic nature, leading to two screws, namely the kinetic and dynamic screws . The angular momentum is not readily determined for arbitrary material systems. However, for rigid bodies, its determination is straightforward due to the simple nature of the velocity field (as a field of moments). We will show that the angular momentum and kinetic energy of a rigid body can be calculated from the body’s inertia operator which quantifies its mass distribution.
