5. INTEGRAL EQUATION AND RELATED ITERATIVE APPROXIMATIONS 

 Identities (4.10a, b, and c) and (4.13) hold for any function (f) continuous in 

 the domain d and on its boundary o + h + c. If the function (p is taken as the veloc- 

 ity potential of flow about a ship advancing at constant mean speed in a regular sea, 

 then the normal derivative 3<t)/8n of (() is given on the hull surface h, and (j) satisfies 

 the Laplace Equation (2.7) in the mean flow domain d and the sea-surface boundary 

 condition (2.8), with p = = q, at the mean sea surface a. Identities (4.10c) and 

 (4.13) then yield integro-dif f erential equations for determining the potential <j) on 

 the ship surface. Specifically, Equation (4.13) becomes 



[l-w(t)](j)(|) = i>it) - L'(|;(t)) (5.1) 



->■ 

 where the waterplane integral w(5) is given by 



w(t) = (f+ie)^ r G(|,x)dxdy (5.2) 



a .■ 



the potential 'Jj(C) takes the form 



i>(t) = I G3ct)/8nda + F^ ( Gn^^ 3(j)/3nd2. (5.3) 



h c 



and the potential L'(C;4>) is given by 



:-A) = I ((l)-(l)^)8G/9nda - 2i(f+ie)F f" 

 h c 



L'(C;<J5) = ((l)-(l).)8G/9nda - 2i(f+ie)F G(<j)-(j)^)t dJl 



y 



+ F^ f[((j)-(t)^)8G/3x-G(t d(p/dl-n t 3(])/9d)]t d£ (5.4) 



J X z y y 



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