266 



VII. DYNAMICS OF ROTATING BODIES. 



49) 



that is 

 50) 



The axis of this, like that of the 

 polhode cone, is the axis of greatest 

 or least inertia. 



Let us find how fast the invariable 

 line revolves around one of the principal 

 axes. Since the invariable axis is fixed 

 in space, its relative motion is equal 

 and opposite to the actual motion of 

 the part of the body in which it lies. 

 If we call A the diedral angle between 

 the plane of the invariable axis and 

 the axis of X and the XY- plane, we 

 may find -^- Projecting H upon the YZ- plane (Fig. 81), the pro 



jection makes with the F-axis the angle A, given by 



Fig. 81. 



51) 

 from which 



Differentiating, 

 52) 



H 



Cr 



C / dr dq\ 1 



BC 



dr ^dq 



Inserting from Euler's equations 31), 



dq _ C A dr _A-B 



~dt ~ B r &' ~dt ~ C 



dl p{B(A-B)q*+C(A-C)r*} 



53) 



dt 



-H* 



f\ A H*-HP l] i = *\*H?-H 



P 



2AT 

 H* 



-1 



-EL\ 2 



- 



sin 2 (H x) 



