f = ca(L/g)^/^ (2.6a) 



F = U/(gL)^/^ (2.6b) 



e = a(L/g)-'-/^ (2.6c) 



The basic potential-flow problem of the linearized theory of ship motions in a 

 regular sea may now be stated. As is well known, the problem consists in solving 

 the Laplace equation 



V^(|) = in d (2.7) 



subject to the boundary conditions specified below. The solution domain d in Equa- 

 tion (2.7) is the domain exterior to the ship hull and bounded upwards by the mean 

 sea surface a. On the mean sea surface a, the boundary condition (2.5) must be 

 satisfied: 



[8 -(f-iF9 +ie)^](}) = i(f-iF8 +i£)p - q on a (2.8) 



I I I I 

 where we generally have p = = q. The potential (j)(x) vanishes as ] |x| |-*- «> at least 



as fast as l/||x||; that is, we have 



(j) = 0(1/1 |x| |) as I |x| |-^ «> (2.9) 



Finally, on the mean position of the ship hull surface h the potential must satisfy 

 the usual Neumann condition 



9(j)/3n given on h (2.10) 



where 9(})/3n = V<})'n is the derivative of <t> in the direction of the unit normal vector 

 n to h, taken to be pointing inside the fluid. The precise form taken by the 



