OF ENERGY IN A SYSTEM OF MATERIAL POINTS. 



733 



If we write 



.(79), 



T) = V V + rx pz 

 =w W+py qx 



then 77, will be the velocity-components of a particle with respect to 

 axes passing through the centre of mass of the system and rotating with the 

 angular velocity whose components are p, q, r. We may therefore call 17, 

 the velocity-components of the internal motion. If the system were to become 

 rigid, the internal motion would become zero. The energy of internal motion 

 may be expressed in terms of 77, , thus : 



h 2 ) (80). 



We have now to express the energy of internal motion of a system of 

 s 1 particles in terms of the quantities U, V, W, F, G, H and T belonging 

 to the system of s particles, together with the position and velocity of the 

 ,$ th particle. 



To avoid the repetition of suffixes we shall distinguish quantities belonging 

 to the minor system of s 1 particles by accented letters, and quantities 

 belonging to the complete system of s particles and the particle m t by unaccented 

 letters. We shall also write 



We thus find 



Mm 



' = MX-mx 



' = MU-mu, 



' = L-p.(y-Y)(z-Z) 



Since the choice of the axes of reference is arbitrary, we may simplify 

 the expressions by taking for origin the centre of mass of the system M, and 

 for the axis of z the line passing through the particle m. We may also turn 



