for the solution of the Laplace equation with the boundary conditions in- 

 cluding nonlinear terms. In order to find such an expression, we apply 

 Green's theorem to the velocity potential (j) and an appropriate Green's 

 function in the space bounded by a closed surface. Figure 3 shows this 



Figure 3 - Coordinate System and Control Surfaces 



enclosed surface to encompass the portion of the hull surface in the lower 

 half space S, a large vertical cylinder I surrounding the ship, the portion 

 of the horizontal plane z = between S and E, E_ and the portion of the 

 sea bottom inside the cylinder I . Then we have 



)(P) = - 



4tt 



S + Z + E 0+ Z B 



G(P,Q) -£ 



M_, 



(Q) 



3G(P,Q) 



3n„ 



d S, 



(10) 



