KINETICS OF A RIGID BODY. [327. 



with the notation of Art. 255. As the axes are fixed in the 

 body (Art. 324), the moments and products of inertia are con- 

 stant ; and it appears from the equations (2), Art. 315, that this 

 expression is the derivative with respect to the time of the 

 component H x of the impulsive couple H that produces the 

 rotation &> at the time /. 



Next operating in the same way on the remaining terms of 

 the component accelerations (i), viz. those arising from the 

 centripetal acceleration, we find 



w^myz) 

 + co^mz 2 ) + o^myz 

 F(D x + Cco y + Da>,} - co y (Eco x + D<o, + Ba>.) 



E(i) x D(d y + Cd) g ) Q) g ( F(0 X + B(D y 



by (2), Art. 315. 



The moments of the effective forces about the other two axes 

 can now be obtained by cyclical permutation of the subscripts 

 x, y, z. Thus we find that the equations (6), Art. 224, assume 

 the form 



(3) 



The reaction A of the fixed point does not enter into these 

 equations ; as it intersects every one of the axes, its moments 

 about these axes are zero. 



327. Geometrically the equations (3) mean that the vector #of the 

 resultant couple of the external forces has two components one of which 

 resolves itself along the axes into dH x /dt, dHJdt, dHJdt, while the 



