II. Researches in the dynamics of a rigid body by the aid of the theory of screws

Abstract

In a paper communicated to the Royal Irish Academy (“The Theory of Screws—a geo­metrical study of the kinematics, equilibrium, and small oscillations of a rigid body,” Transactions of the Royal Irish Academy, vol. xxv. p. 157) the chief features of what the writer has ventured to call the Theory of Screws were sketched. It is the object of the present paper to give some further extensions and applications of that theory. The chief point which it is now proposed to illustrate is the appropriateness of the method to many problems in the dynamics of a rigid body. This will, to some extent, appear from the analogy subsisting between the conceptions of the theory and the familiar notions to which the conceptions degrade when the rigid body degrades to a particle. It should also be remarked that the complete generality of the method with reference to forces and constraints gives rise to many theorems of great interest, which could hardly be enunciated without the ideas which the theory embodies. A screw is a straight line in space with which a definite linear magnitude termed the pitch is associated. The pitch may have any value from —∞ to + ∞. A body is said to receive a twist about a screw when it is rotated about the screw, and is at the same time translated parallel to the screw through a distance equal to the product of the pitch and the angle of twist.