of three Magnetically Coupled Oscillating Circuits. 577 



Let : w 1? m 2 , and m % the masses of the three pendulums ; 

 Gi, G 2 , and G 3 the centres of gravity of the three 



pendulums ; 

 K x the radius of gyration of the pendulum A about 



the axis of rotation, and 

 K 2 and K 3 the radii of gyration of B and C about 



their centres of gravity ; 

 /i ]? /t 2 , and h 3 the distances between the centres of 



gravity and the axes of rotation ; 

 a, b the distances of the points of suspension of B 

 and from that of A ; 

 and let the pendulums be inclined to the vertical at 0. cf>, 

 and yjr respectively. 



In the case of a conservative dynamical system like 

 this, where there are no extraneous forces, b} 7 Lagrange's 

 equations we have for the equation of motion of three 

 pendulums : 



d BT BT BV . . . 



Tt'W~W~- ~W ' ' P endulum A 



„ B. 



• • ., 0. 



Now the kinetic energy of the pendulum A about the axis 

 of rotation is ^mj^^t—j ; 



that of B relative to its centre of gravity is ^??i 2 K 2 2 /-^-\ ; 

 and hence the kinetic energy of B relatively to A is 



d 



dt 



BT BT 

 ' B</>' d<f> ~ 



BY 



B<£>' 



d 

 dt 



BT_BT_ 



B"v/ r/ fi^fr 



_BV 



B^' 



-^@) ,+ *-{^(S + Mf) 



7 </6> ^ -r~t)X 



2ali 2 -77 • 7 • cos 9 — c7 ^ 



Similarly, kinetic energy of C relatively to A is 



**>'(f)-(f)-=<^}- 



PWL %. S. 6. Vol. 43. No. 255. ilfareA 1922. 2 P 



