Fieri and Lee 



where 



K = u, 2 / g 



Since the variable x enters into this problem as a parameter, we 

 take e - lk o XCos P as a constant term and let it be denoted by c 



* D . <T. - - > - o 



<I> d ~ Be Kz + jK °l y l as |y|— =o (81) 



where B is a constant. 



Substituting Equation (80) into Equation (79), we obtain 



^ i / .a \ K„ (z - jy sin/3) 



© = - w AC - n, sin M nj e ° y Jy ' 



Y Dn I _ o v J 2 3 ' 



(82) 



where n and n - are the y and z components of the unit normal 

 vector on c Q . For brevity, we let 



y ' = y sin /3 



(n„ cos K y' - n' sin K y') 

 3 o c o 



(83) 



- j A' e K ° Z (ni cos K y' + n sin K y') 

 J 2 o 3 o 



Since we assume that catamarans are made of two symme- 

 trical hulls, we know that n£ is odd, and n3 is even, with respect 

 to y . Then, it is clear that the real part of the right side of Equa- 

 tion (83) is an even function, and the imaginary part is an odd func- 

 tion. Now, we let 



Y D v e o 



536 



