Motion and Resistance of a Low-Waterplane Catamaran 



Since 



« k M " Re j [ ? ko '"""l 



= Re 

 as defined in Equation (2), we have 



{ 'k = - j " f ko e 



■, [<* te ^« ta )-- , " t ] 



- jwt 



f ? ,. - i co t 



*k = - w^t, e J 

 ko 



in which we have dropped Re: for the sake of brevity; however, it 

 will be understood in the sequal that the real part is meant whenever 

 a term is involved with e~ Jwt . Substitution of the foregoing results 

 into Equations (3) through (7) yields two sets of complex algebraic 

 equations of the form 



A i x i - B i 



A 2 X 2 = B 2 



(8) 



where 



B i = 



'30 



'50 



F (e) 

 3 



F («) 

 h 5 



A i = 



-co (m+a„„)+ C„„ - j co b 

 v 33 ; 33 J 



33 



2 



co A 



53 + C 53 " jwB 53 



X 2 = 



B 2 = 



•20 

 '40 

 '60_ 



-(e)" 



2 



. (e) 



4 



-(e) 



2 



co A + C - 1 w B 



35 35 J 35 



w (i +A ) + C 



v 5 55 y 55 



j w b 



55 



and 



473 



