2 1 9-] GENERAL PRINCIPLES. 1 19 



CHAPTER VI. 



KINETICS OF A RIGID BODY. 



I. General Principles. 



* 218. In kinetics the term rigid body means any system or 

 aggregate of mass-particles whose mutual distances remain 

 invariable. A rigid body may therefore consist of a finite 

 number of rigidly connected particles or of a continuous mass 

 of one, two, or three dimensions. Its motion depends not only 

 on the forces acting on the body, but also on the way in which 

 the mass is distributed throughout the body. * 



In the present section the rigid body is assumed to be free 

 unless the contrary be stated explicitly. 



219. Let us consider any one particle m of the body ; at any 

 time /, let j be its acceleration and F the resultant of all the 

 forces acting on the particle. Then the motion of this particle 

 (see Arts. 35, 67) is determined by the equation 



mjF. (i) 



It should be noticed that among the forces acting on the 

 particle are included not only those external forces acting on 

 the rigid body that happen to be applied at m, but also the 

 .so-called internal forces which would replace the rigid con- 

 nection of the particle m with the rest of the body. 



If, at the time t, x, y, 2 are the co-ordinates of the particle 

 m with respect to a fixed set of rectangular axes, then the 

 components of its velocity v may be denoted by x, y, z\ those 

 of its acceleration j by x t y, z* And if the components of F 



* Here again we shall use this so-called fluxional notation, according to which 

 derivatives with respect to the time are denoted by dots; see the foot-note to Art. 183. 



