Since 



Motion and Resistance of a Low-Waterplane Catamaran 

 F i e) - > >»o Jf u i*l*' 



- P /"/■(*. ° +42. * i^-~% ••*>♦„«• 



M in jw 3n °i5 j o> 2n 16 D 



So 



iKn V S = if ^Dn*i 



ds 



So 

 by Green's theorem and 



<t> = - 4> n on S 



In Dn o 



from the kinematic boundary condition, we can show that 



>//ijo, n. + (*•+— 4>, a.,.-!^*, a.J_a_l(D T 

 JJ\ ° i i i 03 3 i5 j w 2 i6 d n / x 



So (72) 



The above procedure for eliminating the diffraction potential (J) D 

 from the expression for the wave -exciting force and moment was 

 first shown by Haskind (1957) for zero speed and later it was exten- 

 ded by Newman (1965) for the case of forward speeds and is referred 

 to as the Haskind-Newman relation. 



Similarly, we can derive 



F ( m ) = p y 



So 



= - " E «W„ ff <*• + ™ *, '•R-^*, «-*)*v d « 



/-^ko // in iw 3n i5 1 w 2n 16 k 



k=2 "so 



t<- -^ ( m ) • , ,• 



If we express F . in the form 



6 



F M = E I ( a, 2 A., + j«B. v ) 

 1 k:2 ko v ik J ik 



where A ft are the so-called added mass quantities, and B:j< 

 are the damping quantities, we find from Equation (73) that 



A., = Re 

 ik 



j ( c>> 2 ff in ju 3n "i5 j « 2n 16 k j 



So 



531 



