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BELL SYSTEM TECHNICAL JOURNAL 



which determines d as a function of v? and /. From (2a), neglecting the first 

 term as above, 



M = S [ ^ cos 9 dt, 

 J dt 



and the restoring torque about y, or 



Ty — —S cos 6 I 



d<p 

 It 



cos 6 dt. 



(12a) 



This, together with (11a), determines Ty as a function of ip and /, instead of 

 <p alone as it is for infinitesimal displacements. 



Fig. 3 — Diagram showing the displacement of the axes of a gyrostat. 



We assumed here that, in the rest ])osition of the rotor, its B axis coin- 

 cides with that of the ai)i)lied displacement if. When this is not the case, the 

 relations arc more complicated, but (hey should be qualitatively the same. 

 Hence, for an element of the medium, the torcjue per unit volume should 

 be a function of <^ and / sirnilar to T,, , which reduces to —4tj(i(^ for very small 

 displacements. Since the restoring torque is in the direction of v? we may 



