Kinematics

Abstract

In continuum mechanics, we are interested in material bodies that can undergo motions and deformations. The stage for such phenomena to occur is, of course, the four-dimensional space-time. In this book, we shall restrict our attention to the Newtonian space-time of classical mechanics. The Newtonian space-time W can be regarded as a product space of a three-dimensional Euclidean space £ and the one-dimensional space of real numbers ℝ through a one-to-one mapping

$$ \phi :W \to \varepsilon \times R $$

Such a mapping is called a frame of reference. To set the stage for any discussion hereafter a frame of reference is always chosen, either explicitly or implicitly. We will usually think of a frame of reference as an “observer”. Different observers will measure space-time events in different ways. The relation between two different frames of reference will be discussed later.