Brard 



W;(t') = -piyL r roj(T,')d77' r ^•i^M) Fi(T')dT' 



*-^o 1 



*;■«') = p I [(ff)., r>.°*) + (n)„. «^;(-'' 



O'mAn(m) dS(m) 



The resulting moment is 



i;(t') = iy Jn;(t') = .- ^ 5P [^i^t') + w'i^t'>] • 

 Because ^'(/x) is independent of t', we have 



)n;(t')=puj TqiCt]') Xx(75')xd7)' (g)p^ F*(t') + I ^ (g)^^ F*(t'-T')dT' 



(Iq J + 



"'^L dr (u) , JJ ^*i<^'"'0+^ [^(^'"^ n(m)i^ - x(m) n(m)ij dS(m) 

 '^ s 



-P L (u) JJ bT' ^'^i^^'"'*'^ C^^*"^ n(m)i^-x(m) n(m)i^] dS(m) 

 ^* s 



-p- — fgj ^dr'JJ — S7*(m, t'-r') [z(m) n(m)i^- x(m) n(m)i^] dS(m) 



+ ■^ ' s 



t' 



+ J ^ (^) , S^iC-"' t'-r')dT' i^n(m) dS(m) 



It is assumed here that the moving axis coincide at time t ' with the fixed 

 axis, and the moment is referred about the latter. The last term comes from 

 the derivative 



d 



— a m An(m) . 



In the quasi -steady motion, the moment is 



856 



