Kinematics of a Particle

Abstract

Dynamics is the branch of analytical mechanics devoted to the study of the motion of bodies and thc forces and torques that may produce it. However, sincc geometric considerations play a principal role in dynamics, we shall consider initially only the purely geometrical aspecls of motion. The theory of motion without regard to the agents that produce it is called kinematics. Kinematics is the geometry of motion. Thus. in this chapter we set the stage for future developments by making precise the idea of motion and its relation to velocity and acceleration. These definitions subsequently are applied to describe the general motion of a material point in terms characterized by the geometry of the curve along which the point moves. After the basic kinematical ideas are explored thoroughly for a rigid body in Chapters 2 and 3 and for moving reference Systems in Chapter 4, we shall proceed to investigate the relation of forces and torques to the motion of bodies. Let us begin with a discussion of some primitive terms needed in our work.

Mathematics deals exclusively with the relations of concepts to each other without consideration of their relation to experience. Physics too deals with mathematical concepts; however, these concepts attain physical content only by the clear determination of their relation to the objects of experience. This in particular is the case for the concepts of motion, space, time.

I believe that the first step in the setting of a “real external world” is the formation of the concept of bodily objects and of bodily objects of various kinds.

Albert Einstein,

Essuys in Physics

The erratum of this chapter is available at http://dx.doi.org/10.1007/978-1-4899-7285-9_5/10.1007/978-1-4899-7285-9_5