Physics of Discrete Systems
MECHANICS, sometimes vaguely called the science of motion, is a discipline which deals with all experience that can be represented and understood with the use of three kinds of system: (1) mass points (more loosely called particles) or sets of mass points; (2) rigid bodies; (3) deformable, continuous material media. Accordingly, the subject has three large branches, point mechanics, mechanics of rigid bodies, and mechanics of continua. It is true, of course, that these systems are often considered in motion, but the conditions under which they are at rest are just as important as is a description of their motion. We shall take up the three subjects one after another. Most space will be allotted to the first because it sets the stage for the other two, many of the principles of point mechanics being utilized in the other fields.
A mass point, or particle, is a very convenient idealization which can be set in correspondence with a great deal of our experience. In practice we often forget its idealized character and take it to be an object in the usual sense, like a stone or a flower. It is indeed one of the most obvious systems of the whole of science and has its place in the C field very near the P plane (cf. Fig. 6.1). From the infinite variety of properties (position, color, odor, taste, perhaps its chemical composition) which might be assigned to it, mechanics chooses a very limited set as being of physical interest. A mass point has one intrinsic property which never changes (we are not at present concerned with the relativistic modification of point mechanics), its mass; in addition it possesses position and velocity. If the particle has its full range of motion, each of these must be broken down into three individual properties or components, the position into the three coordinates x, y, z measured from some chosen origin, the velocity into its components vx, vy, vz. In the