516 



On the Action of Coupled Circuits. 



7. The differential equations of the problem are also 

 formally reproduced when 



2U = ^ 2 /R + ?/ 2 /S. 

 These suggest the mechanism represented in fig. 3. Here a 



Fisr. 3. 



heavy ring is pivoted on an axis AB, about which it can 

 turn with a spring connexion. It carries the axis CD on 

 which is pivoted a heavy concentric sphere, also with a 

 spring attachment. If the axes CD, AB are inclined at an 

 angle #, while the ring rotates about AB through an angle sjr 

 and the sphere rotates about CD through an angle (/> relative 

 to the ring, the mechanism presents a framework of Eulerian 

 angles. The rotation of the sphere about AB can be resolved 

 into components i/r cos 6 about CD and ijr sin 6 about the 

 perpendicular axis. Hence if C is the moment of inertia of 

 the sphere about any axis and B is the moment of inertia 

 of the ring about AB, the kinetic energy of the system is 

 given by 



2T = C(<j> + yjr cos 6>) 2 + C^ 2 sin 2 + Bijt* 



= C</> 2 + 2C0f cos + (C + B>p. 



