CHAPTER VII. 



SYSTEMS OF FORCES. 



114. Conception of a rigid system. We can imagine that 

 a system of particles moves in such a way that the distance 

 between any two particles of the system is constant. Such a 

 system is said to be rigid. 



In particular if the particles of a rigid system continuously 

 fill a surface the system is a rigid body, and the surface is the 

 surface of the body. 



In a rigid system the motion of the whole system is determined 

 when the motion of three of its particles is determined. For the 

 three particles determine a frame of reference relatively to which 

 all the particles of the system have invariable positions. 



To determine the positions of all the particles of a rigid 

 system relative to a frame is therefore the same thing as deter- 

 mining the position of one frame, F, relative to another. This 

 requires the determination of the positions of the origin 

 of the frame F, of one of its lines of reference, and of a 

 plane through that line. The position of a point depends on 

 three quantities, the coordinates of the point. The position of a 

 line through a point depends on two quantities, since the line 

 may make any angle with one of the axes, and the plane through 

 it parallel to that axis may make any angle with a coordinate 

 plane, but these two angles determine the line. The position of a 

 plane through a line depends on one quantity, which may be 

 taken to be the angle it makes with the plane drawn through 

 the line parallel to one of the axes of reference. Thus the 

 positions of all the particles of a rigid system relative to a frame 

 are determined when six quantities such as those specified are 

 given. 



It follows that the velocities and accelerations of all the 

 particles of a rigid system must be expressible in certain definite 



