Brard 



h'%[(t') = puj r,,(77') x(T7')d77' |(J)^^ [1-F*(0)] 



^0 1 







+ p\J JJ n(m)i^ dS(m) J (§) ^ [Sy^Cm.+co) - S7;(m,0)] 



s L t ' 



+ r* /^J Jl. [Sy^Cm.+co) - Syl(m, t'-T')]dT'| 



+ p^ Jj[z(m) n(m)i^-x(m)n(m)iJS(m) J(^) ^ ^ 7*i(m,0) 

 s "^ 



Let 



"..K)., = I'^'^LU^a;!^)^, (36) 



be the moment in the quasi -steady motion. We have 



' = _2_ 

 'i ALU 



J r ^^^(77') x(v')dv' + If [yi(m,0+) + S7;(m,+co)] i^n(m) dSCm) I . (37) 



Then, putting 



7 J f r^iCr,') x(77')d77'[l-F*(t" 



JJ [S7*j(m,+co) - Sy^Cm.t')] n(m) i^ dS(m) 

 s 



JJ ^ ^^1*^""'^'^ t^*^"''' "^'"^^x-'^C'") nCm)i,] dSCm)l , (33) 



+ 



s 



we have 



858 



