304 



MOTION OF KIGID BODIES 



i- tr 



GENERAL EQUATIONS OF MOTION OF A KIGID BODY 



249. Let be any point of a rigid body, and let Ox, Oy, Oz be 

 a set of axes moving so that the point maintains its position in 

 the rigid body, while the axes remain parallel to their original 



position. 



Let the velocity of have compo- 

 nents u, v, w along these axes. The 

 motion of the rigid body relative to 

 these axes will be a motion of rotation 

 about some axis OP which passes 

 through 0. Let us regard this as 

 compounded of rotations co x , co y) &> 2 

 about the three axes. 

 Let x, y, z be the coordinates of any point of the rigid body rela- 

 tive to these axes. The velocity of this point relative to the frame 

 supplied by the axes moving with has components 



L/r 



FIG. 149 



dx 



_ 

 dt 



dz 

 dt 



while the velocity of this frame in space has components 



v, 



Thus the whole velocity of the point x, y, z has components 



dx 



37 

 dt 



dt 



At any instant let L, M, N denote the sums of the moments of 

 the external forces about the axes of x, y, z respectively, so that, as 

 in 243, 



etc. 



The moment of momentum of a particle of mass m, at x y y, z y 

 about the axis of x is 



dy\\ 

 *)\ 



