Pi en and Lee 



paper is derived in, e.g., Wehausen (197 1 , pp. 243-245). To be 

 compatible with the complex expression on the right side of Equation 

 (1), the motion displacements ^ are assumed to be complex functions 

 in the form of 



where Rej means that the real part of a complex function in terms 

 of the imaginary unit of j should be taken, and £ and £ are 

 real functions. 



Each hull of the catamaran is assumed to be slender so that 

 the change of the surface normal in the length direction is small 

 compared to the change in the transverse directions. This slender- 

 ness assumption together with the symmetry of the two hulls lead to 

 decoupling motions into three independent groups of motion : (1) sur- 

 ge, (2) heave and pitch, and (3) sway, roll and yaw. In this work the 

 surge motion will not be considered. The explicit forms of the remai- 

 ning two groups of motion are given as follows. Heave and pitch 

 equations : 



(M + A 33> V ^3 V ^ { 3 + ^5 h* ^ V C 35 f 5= ^ •" 1 "' < 3 > 



«, + A 55 ) {,♦ ^ l 5+ C 65?5+ ^ 3f, + B 53 j 3 ♦ Sj h - F< e » .*»« 



(4) 

 Sway, roll, and yaw equations : 



(M + A 22 } V B 22 *2 + ( A 24 - Mz g ) ^ +B 24^4 + A 26 i; + B 26 l 6 = 



F 2 (e) e- j0,t (5) 



( J 4 + A 44 } ^ + B 44 h + C 44 *4 + < A 42 " ^ g ) ^+ ^2 * 2 



+ \sh + B 46*6 =F 4 (e) e- jWt (6) 



(I 6 + A 66 } *6 + B 66 *6 + A 62 h + B 62 *2 + * S J* + B 64 *4 = 



(e) - j ut . . 



E> ' e (7) 



470 



