8 - Rigid body dynamics

Summary

The concept of a rigid body

Most simple elements and compounds exist in three possible states, gaseous, liquid and solid. According to the methods described in the previous chapter, the motion of bodies composed of matter in any of these states can be described in terms of a large number of small particles. The motions of gases and liquids have been briefly discussed at the end of the last chapter, and we turn now to consider the motion of solid bodies.

In general, solid bodies have a very complicated structure, and in their motion some parts move relative to other parts. However, in many applications, particularly in mechanical problems, the component parts of a body move in an approximately rigid way. Thus it is convenient to introduce the concept of a rigid body as a theoretical idealisation. This may be defined as follows.

Definition 8.1.A body is said to be rigid if the distance between each of its constituent points remains constant, irrespective of the motion of the body as a whole or the forces that act upon it.

Of course no physical body is exactly rigid. Even objects made of solid steel bend or deform slightly when acted on by external forces. But when considering the motion of solid objects, it is often convenient to regard them as being perfectly rigid, at least as a first approximation. Thus, in all applications of the study of rigid body dynamics, there must always be an initial simplifying assumption that the body under consideration should be regarded as being perfectly rigid.