Outer Problem 



The outer solution can be constructed from a suitable distribution of source 



strength along the longitudinal x-axis. If we denote the source strength with q.(x) 



then the outer solution is expressed in the form 



f. = ( q.(?) G(x-5,y,z) d^ for j = 3 and 5 (43) 



Here, we consider the solutions for heave and pitch only. The Fourier transform of 

 Equation (43) is derived from the convolution theorem in the form 



v.* = q.* G*(y,z;k,K) (44) 



where G* is defined by Equation (39). The inner approximation of Equation (44), for 

 small values of the coordinates (y,z), can be constructed by substitution of Equation 

 (41) 



^.* = q.* G_^ - - f*q.* (45) 



J ^j 2D IT ^j 



Inner Problem 



The fundamental solution of the inner problem is that of the strip theory. 

 However, the matching requirement with the outer solution will differ from the 

 condition of outgoing radiated waves satisfied by the strip theory. Because the 

 outer solution includes a longitudinal function of x which depends upon the three- 

 dimensional shape of the ship hull, we solve the inner solution in the following 

 form 



'P. = <P^^'* + C.(x)((J).+(J).) (46) 



where C.(x) is a function to be determined by matching with the outer solution and 



(s) .-^ 

 *p . is the strip theory solution which can be expressed as follows 



11 



