45 



CHAPTER VI. 



THE PRINCIPAL SCREWS OF INERTIA. 



51. Introduction. If a rigid body be free to rotate about 

 a fixed point, then it is well known that an impulsive 

 couple in a plane perpendicular to one of the principal 

 axes which can be drawn through the point will make 

 the body commence to rotate about that axis. Suppose 

 that on one of the principal axes lay a screw rj with a 

 very small pitch, then a twisting motion about rj would 

 closely resemble a simple rotation about the correspond- 

 ing axis. An impulsive wrench on ij will, when united 

 with the reaction of the fixed point, reduce to a couple 

 in a plane perpendicular to the axis. If we now sup- 

 pose the pitch of TJ to be evanescent, we may still 

 assert that an impulsive wrench on TJ of very great in- 

 tensity will cause the body, if previously quiescent, to 

 commence to twist about rj. 



We have stated a familiar property of the principal 

 axes in this indirect manner, for the purpose of showing 

 that it is merely an extreme case fora body with freedom 

 of the third order of the following general theorem : 



If a quiescent rigid body have freedom of the n th order, 

 then n screws can always be found (but not more than n\ such 

 that if the body receive an impulsive wrench on any one of 

 these screws, the body will commence to twist about the same 

 screw. 



These n screws are of great significance in the pre- 

 sent method of studying Dynamics, and they may be 

 termed the principal screws of inertia. In the present 

 chapter we shall prove the general theorem just stated, 



