and 



d<P ^ 2 



— h~-f~ v? 7 (s) = ° on z = ° (21) 



9 ^7 (S) 3 *>o 



— » = - -s — on the body surface (22) 



dn dn J 



Here (p is the potential of the incoming wave given by 



<£> = - -^ exp (K z+iK x cos 3-iK y sin 3) (23) 



where A = the amplitude of the incoming wave 



3 = the heading angle of the incoming wave (3 = 180° is for a 

 head sea, and 3 = 0° is for a following sea) 



K Q = oi o 2 /g 



(S) 



The solution of <P 7 satisfying Equations (20)-(22) is 



V^ " I °d G 2D d£ i24) 



where G, is the complex source strength at the ship's contour c, and G„_ is given by 

 Equation (17) . 



UNIFIED SLENDER-BODY THEORY 



4 

 The velocity potential due to oscillation is given by Newman as 



v. =^ j (s) + c -j (x) ( VV (j=3 ' 5) (25) 



where <\> . is the conjugate of <}> . . The coefficient C.(x) is expressed by the integral 



