P-Len and Lee 



have to obtain the solution of (t> D before we can evaluate complete 

 hydrodynamic loadings. In Appendix B, the method of solving (j) D 

 by source distribution similar to that used in solving the motion 

 potentials (b k is given. We shall not attempt to reduce the last inte- 

 gral of the right side of Equation (44) to added inertias and dampings. 

 However, attention should be paid to the fact that decoupling between 

 the motions of the vertical and horizontal planes can no longer be 

 made in this integral. This is because we are dealing only with one 

 hull for which there exists asymmetric pressure distribution even 

 for a symmetric demihull, due to the blockage effect of the other 

 hull. Thus, every term of the summation in Equation (44) would sur- 

 vive. 



Applying the foregoing results into Equations (35) and (36), 

 we obtain the following expressions 



V 4 (0)=- * 2 m '(? 20 + x i M - z'« 40 ) 



r ( 45 ) 



+ p E lJ <!>~<fc di - j.p / ( « jb T + a, <b ) n dt 



*ko( 2 A di -^/"(-aV-V-a 



k=2 



~Cr 



- J P 



'Cr 

 + P 



>/ ( «b <t>j + w 4> D ) n 3 di 

 C R 



At f cb cb d 



22 K ko / T 3n ^k 

 k = 2 X_ 



(46) 



+ 2pga( ^ 30 -x $5Q + b ^ 4Q ) 



M l( 0)=- c 2 [r +m . (^(.-h/^^ 



-jpj Uo ( t ) I + w <V {^3 + (h " z) n 2 } d ^ 

 + * E « ko / ^4n \ d * 



+ 2Pgab(^ 3() -x € 5() ) + pg S^ GM 1 ^ 4Q (47) 



486 



