CHAPTER IX. 



THE DYNAMICS OF A RIGID BODY, WHICH HAS FREEDOM 

 OF THE FIRST ORDER. 



78. Introduction. In the present chapter we shall 

 apply the principles developed in the preceding chapters 

 to the examination of the Dynamics of a rigid body which 

 has freedom of the first order. The ensuing chapters 

 will be similarly devoted to the other orders of freedom. 

 We shall in each chapter first ascertain what can 

 be learned as to the kinematics of a rigid body, so 

 far as small displacements are concerned, from merely 

 knowing the order of the freedom which is permitted by 

 the constraints. This will conduct us to a knowledge of 

 the screw complex which exactly defines the freedom 

 enjoyed by the body. We shall then be enabled to 

 determine the reciprocal screw complex, which involves 

 the theory of equilibrium. The next group of questions 

 will be those which relate to the effect of an impulse 

 upon a quiescent rigid body, free to twist about all the 

 screws of the screw complex. Finally, we shall discuss 

 the small oscillations of a rigid body in the vicinity of a 

 position of stable equilibrium, under the influence of a 

 given system offerees, the movements of the body being 

 limited as before to the screws of the screw complex. 



79. Screw Complex of the First Order. A body 

 which has freedom of the first order can execute no 

 movement which is not a twist about one definite screw. 

 The position of a body so circumstanced is to be specified 

 by a single datum, viz., the amplitude of the twist about 

 the given screw, by which the body can be brought 



G 2 



