. : 



BO 41 i i: IS* I>I-II:II:ITIUN 



We- shall find it uaeful in what follows to define the energy of internal 

 M the exce of the whole kinetic energy of the system over that 

 which it would have if it were moving like a rigid body with the same con- 

 the ame components of momentum and of angular momentum. 



If we Mippoeo the internal motion of the system to be destroyed in a 

 abort tirw by internal forces, so that the configuration is not sensibly 

 ahcmi during the process, then the work done by the system against these 

 foMOt i the measure of the energy of internal motion. 



Writing 7* for the kinetic energy referred to the origin, K for that of 

 the maw moving with the velocity of the centre of mass, J for the kinetic 

 due to the rotation of the system as a rigid body, and 7 for the 

 of internal motion, we have 



where 



I=T-K-J 



J= 2 ftro ( 



W) 



(71), 

 (72), 

 (73), 

 (74), 



where p, q, r are the components of angular velocity with respect to the 

 axes of x, y, z and are related to F, G, H by the equations 



aF-nG-mH=p, 

 -nF+bG- lH=q, 



Ap-Nq-Mr = 

 -X r + Bq-Lr = 

 -Mp-Lq+ Cr = 



-mF- 



clt=r, 



(75). 



-. :.- 



ft -2i - 



= -m(y-Y)(z-Z) 



=Si (z-Z)(x-X) [...(76). 



Writing for the sake of brevity 



-1, -N, -M 

 -N, B, -L 

 -M, -L, C 



d= 



a, n, m 



n, b, I 



m, I, c 



(77), 



the relations between the moments and products of mobility and those of 

 inertia will be given by equations of the forms 



> = BC-D Ad=bc-f 



Dd=l. 



Ld= mn al, 



.(78). 



