CHAPTER VII. 



THE PRINCIPAL SCREWS OF INERTIA*. 



78. Introduction. 



If a rigid body be free to rotate about a fixed point, then it is well known 

 that an impulsive couple about an axis parallel 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 there was on one of the principal 

 axes a screw ij with a very small pitch, then a twisting motion about 77 would 

 closely resemble a simple rotation about the corresponding axis. An impul 

 sive wrench on 77 (i.e. a wrench of great intensity acting for a small time) 

 will reduce to a couple when compounded with the necessary reaction of the 

 fixed point. If we now suppose the pitch of 77 to be evanescent, we may still 

 assert that an impulsive wrench on it] of very great intensity will cause the 

 body, if previously quiescent, to commence to twist about ?;. 



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 for a 

 body with freedom of the third order of the following general theorem : 



If a quiescent rigid body have freedom of the nth order, then n screws can 

 always be found (but not generally more than n), such that if the body receive 

 an impulsive wrench on any one of these screws, the body will commence to 

 tiuist about the same screw. 



These n screws are of great significance in the present 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, while in the 

 chapters on the special orders of freedom we shall show how the principal 

 screws of inertia are to be determined for each case. 



* Philosophical Transactions, 1874, p. 27. 



