REFLECTION OF DIVERGING WAVES 



381 



Fig. 1 — Diagram of a gyrostat, showing its axes of rotation. 



C about y. To study its effect we make use of Euler's equations for a rotating 

 rigid body.^ 



A~' - {B -C)a,2C03 = L, 

 at 



B 



It 



- (C - ^)C03C01 = M, 



C^ - {A - B)o}ico2 = N, 

 at 



where wi , C02 and 0)3 are the angular velocities about three principal axes of 

 inertia, fixed in the rotor, the moments of inertia about which are A, B 

 and C, and L, M , and .V are the accompanying torques about the three axes. 

 They are also at any instant the values of the torques about that set of 

 axes, fixed in space, which, at the instant, coincide with the axes 1, 2, 3, 

 which are fixed relative to the body. We let the 3 axis coincide with the 

 spin axis C. We choose as the 1 and 2 axes, lines in the rotor which, at the 

 instant, are in the x and y directions respectively. Since the moments of 



'Jeans, Theoretical Mechanics, Ginn and Co.. p. 308. 



