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CHAPTER I - KINEMATICAL PRELIMINARIES

Published online by Cambridge University Press:  05 August 2012

E. T. Whittaker
Foreword by
Sir William McCrae
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Summary

The displacements of rigid bodies.

The name Analytical Dynamics is given to that branch of knowledge in which the motions of material bodies, considered as due to the mutual interactions of the bodies, are discussed by the aid of mathematical analysis.

It is natural to begin this discussion by considering the various possible types of motion in themselves, leaving out of account for a time the causes to which the initiation of motion may be ascribed; this preliminary enquiry constitutes the science of Kinematics. The object of the present chapter is to establish a number of kinematical theorems which will be required in the rest of the work.

Kinematics is in itself an extensive subject, for a complete account of which the student is referred to treatises dealing exclusively with it, e.g. that of Koenigs (Paris, 1897). In what follows we shall confine our attention to theorems which are of utility in the applications of Kinematics to Dynamics.

We shall say that a material body is rigid when the mutual distance of every pair of specified points in it is invariable, so that the body does not expand or contract or change its shape in any way, although it may change its position with reference to surrounding objects.

If a rigid body is moved from one position to another, the change of position is called a displacement of the body.

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A Treatise on the Analytical Dynamics of Particles and Rigid Bodies , pp. 1 - 25
Publisher: Cambridge University Press
Print publication year: 1988

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