Description of Motion

In this chapter we are concerned with the motion of continuous bodies without reference to the forces producing the motion. A continuous body is a hypothetical concept and is a mathematical model for which molecular structure is disregarded and the distribution of matter is assumed to be continuous. Also it may be regarded as an infinite set of particles occupying a region of Euclidean point space E3 at a particular time t. The term particle is used to describe an infinitesimal part of the body, rather than a mass point as in Newtonian mechanics. A particle can be given a label, for example, X, and there is a one-one correspondence between the particles and triples of real numbers that are the coordinates at time with respect to a rectangular Cartesian coordinate system.

There are four common descriptions of the motion of a continuous body:

1. Material description. The independent variables are the particle X and the time t.

2. Referential description. The independent variables are the position vector X of a particle, in some reference configuration, and the time t. The reference configuration could be a configuration that the body never occupies but it is convenient to take it as the actual unstressed undeformed configuration at time t = 0. The term natural reference configuration is used to describe the unstressed undeformed configuration at a uniform reference temperature.

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