00 TT — 



ii if f (z+C)u-i w u JQ 



G(x,y,z;?,n, ? ) = ±-f +1 du H_S d| (3Q) 



1 J J u-(v^ u cos 9+v/k) 



-TT 



— 2 



Here, w = (x-£) cos 8 + (y-n) sin 6, and m = u /g. 



By substituting Equation (30) into Equation (29), G (x, 0,0, 0,0,0) = G (x) is given by 



1 I , I (/K+/m u cos 6) .. . | . ■ ... ...... 



G,(x) = 2rf - 5 J 



(/K+i/m u cos 8) exp(-i x u cos 8) 



u - (v/K+/m u cos 8)' 



The diffraction potential of the unified slender-body theory is given by 



<P 7 =^ 7 (S) + C_(x) (<f> +^ ) (32) 



II I s s 



(S) — 

 where <J> is the symmetric function of <f 7 , (J) is the conjugate of (J) , and C 7 (x) is 



Jv 



2 ™7 L 



Here, q 7 is the solution of 



1 (x) - i[-Z_Z-] q (£) f( x _£) dC = - a 

 \ 2 ™7 / L 



(34) 



in Equation (32) can be expressed as 



•s - G 2D 0) °7 « 5) 



10 



