Chessin — On the Motion of Gyroscopes. 25 



n—Clco^Of 

 (11)' aG'^ = k— ij^K • id 



where we have put 



(12) ^3 = 2h— 01^ 4- 2a>l^ — d<o^ 

 From (11)' we find 



r^ 



/ Vd-^bsm^e de 



(13) ^ = ±i/a I 1/Z3 {d + b sin2 6) — {\— CI, cos 6)'^ 



e. 



Formula (13) shows that t is expressed in function of d by 

 a quadrature which involves, in general, hyperelliptic integ- 

 rals. This is the reason why in the treatment of the present 

 problem it has been customary to neglect the mass of the rings 

 ( C7j) and ( C^) of the gyroscope. In fact, if we put A^ — A^ 

 = (7, = C^ = 0, we shall have d = 0, 



s 







sin Ode 



i 



and the integration may be performed with the aid of circular 

 functions. But it is not at all necessary to perform the inte- 

 gration in order to get an idea of the character of the motion 

 in the general case, as we will now proceed to show. 



Let us put 



A = CV + hl,, 8 = y-/, [(6 + rf) A _ 6/,^] , 

 m = 



(14)<! ,„ _ Ghh - ^ ri= <^^i^. + ^ 



