CHAPTEK IX 

 MOTION OF SYSTEMS OF PARTICLES 



EQUATIONS OF MOTION 



176. The present chapter will deal with the motion of systems 

 of particles, taking account of the actions and reactions which may 

 be set up between the different pairs of particles. As a prelimi- 

 nary to this, it will be convenient to recapitulate the results which 

 have been obtained for a single particle, stating these results in a 

 more analytical form than before. 



The whole system of forces which act on a particle must, 

 since they act at a point, have a single force as resultant. Let 

 us call this resultant P, and denote its components along three 

 rectangular axes by X, Y, Z. 



Also the particle, being regarded as a point, must have a definite 

 acceleration /, and, since / is a vector, this acceleration may be 

 supposed to be compounded of three components f x ,f y ,f e along the 

 three coordinate axes. 



The second law of motion supplies the relation 



P = mf. (65) 



We are, however, told more than this by the second law of 

 motion : we are told that the directions of P and of / are the same. 

 Let X, ft, v, be the direction cosines of this single direction, then 

 we have X=XP, Y=pP, Z=vP, 



and also f x = X/, /, = pf, /, = vf. 



From these relations, combined with relation (65), we clearly 

 have = 



Y=mf 



(66) 



220 



