196 Non-Spherical Masses—Dynamical Principles [ch. vii 
A(Tf-w/) = o 
.(179*2). 
With the value of U given by equation (176*5) we have 
Using the value of T given by equation (176‘7) and keeping co constant, 
These are the equations of motion relative to rotating axes. They differ 
from the simpler equations appropriate to the case of w = 0 in two respects; 
first by the presence of what we may call “gyroscopic” terms such as fiisoodx 
and second, by W — ^ co 2 I replacing the potential energy W of the simpler 
equations. 
179. The system will be in equilibrium relative to the moving axes if 
Òl =02 = ... = 0, 
so that, from equation (178*2) the configurations of relative equilibrium are 
determined by the equations 
so that 
Also 
so that 
— = 22m 
dd s 
If we put 
so that fi rs = — fi sr and firr = 0, we obtain 
..(1781). 
so that the equations of motion (177*2) become 
equations of motion (177*2) become 
(178*2). 
^ ( W- £o>*/) = F„ etc. 
(1791). 
When there are no externally applied forces, these reduce to