2 T0 MOTION OF A VARIABLE SYSTEM. [374. 



CHAPTER VII. 



MOTION OF A VARIABLE SYSTEM. 



374. In the present chapter we shall consider very briefly 

 the motion of a general system of n particles, connected in 

 any way whatever, subject to any conditions or constraints, and 

 acted upon by any forces. 



The forces can be distinguished as external and internal. 

 The latter are exerted by certain particles, or groups of parti- 

 cles, of the system on other particles of the same system, while 

 the former proceed from without the system. Thus, in con- 

 sidering our solar system, the attractions between its various 

 members are internal forces, while the attractions of the fixed 

 stars on the sun or planets would represent external forces. 



Besides these two kinds of forces there may be forces re- 

 placing constraints, such as reactions of fixed points, lines, or 

 surfaces, friction, etc. 



I. Free System. 



375. If the system be free, i.e. if it be only acted upon by 

 external and internal forces, while there are no constraints 

 or conditions prescribed for it, the establishment of the general 

 equations of motion is simple, although their integration gen- 

 erally presents insuperable difficulties. The problem of two 

 bodies (Arts. 150-158) is the simplest special case. 



The general principles laid down in Arts. 218-238 for the 

 motion of a rigid body apply almost without change to a free 

 system of particles ; indeed, they apply even to a constrained 

 system, provided that all conditions and constraints are replaced 



