KINETICS OF A RIGID BODY. [315. 



The resultant momentum has evidently the components 



where Jr, y, ~z are the components of the velocity of the cen- 

 troid at the time /, and Mis the mass of the body. Hence the 

 equations (19) become 



(i) 



These equations serve to determine the impulsive pressure 

 A = ^A^+Af+A? on the fixed point O in magnitude and 

 direction. 



315. To form the moment ^m(yzzy) of the momenta of 

 the particles, i.e. the angular momentum of the body, about the 

 axis of x y we resolve the angular velocity co into its components 

 ox,, ft) y , co t along the axes and observe that the components of the 

 linear velocity of any point (x, y, z] arising from the rotation 

 .are (Part I., Art. 293) : 



Substituting these values, we find 



2 m (y'z zy) = w^my 2 (o^mxy a^mzx + 

 or with the notation of Art. 255, 



2m (y'z zy)=Aw x Fw> y Ew t . 



Forming in the same way the angular momenta about the axes 

 of y and z> we find the equations (20) in the form 



A co x Fco y E(D Z = H n 



- Fa> x + B<* y - D< z = H y , (2) 



co x Dw y -f Cco z = H z . 



316. It appears, then, that the rotation of angular velocity 

 co about the axis 1 can be regarded as due to an impulsive couple 

 H whose components are given by (2). Conversely, the effect of 



