Let a body, at time t = t 0, occupy a region of the physical space. To study its motion and deformations, we need to identify its infinitely many points or particles. We name a material particle by the coordinates X i, with respect to a fixed rectangular Cartesian coordinate system, of the point in space where it is located at time t o . Because the triplet ( X 1, X 2, X 3) has a unique value for each point of space, we have devised a scheme for distinguishing among the infinitely many material particles of the body. The triplet ( X 1, X 2, X 3) can be thought of as the name of the material particle P. Henceforth the triplet will simply be stated as the material particle P or the point P. Under a motion of the body, such as that shown in Fig. 3.1, the material particle P moves to the position P ? whose coordinates with respect to the fixed rectangular Cartesian coordinate axes are x i. Then the equation
describes the path of the particle that at t = t 0 is located at X i. The configuration at time t 0 is called the reference configuration of the body and that at time t the present configuration. The triplet (
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