GENERAL EQUATIONS OF MOTION 305 



Hence, by the theorem of 243, 



dt 



and there are similar equations for the other axes. 



250. Relative to the moving axes of coordinates the particle m 

 has coordinates x, y, z, so that a rotation co x about Ox gives the 

 particle a velocity of components 



0, - o>^, 



Similarly the rotations a> y , (o z give velocities respectively of 



components n 



(o y Zj U, co y x, 



and o)^, & s x, 0. 



Compounding these velocities, we obtain as the components of 

 the resultant velocity, relative to the axes, 



2,77 w*^.- - - 



&=*-,* 



dt 



-Tt = a >*y- <v x ' 



and on differentiation of this equation with respect to t, we obtain 

 as the value of part of the left-hand member of equation (127) 



X/ 2 , 2\ a X^ w X^ s 



m (?/ + 2T) - > m xy u > m xz = 

 ; dt *4 ' fa 4 dt 



2m yz(<o* - o>/) +m(^ - ^)o) y 2 



dt dt ' dt 



