and the diffraction pitch moment is 



, icot . - 



h^e = - i2pa) 



r/ y \ iK^X [ \^ f \ 



I A (x+ -:— j e dx e I n„ cos K y-n„ sin 3 sin K y j cfo d£ 



2p C^(x) dx J (iOJn^x+Un^+m^x) Re[(|) ] dl (95) 



Equations (90), (91), (94), and (95) represent the heave force and pitch moment 

 of the bare hull of the SWATH ship. The exciting forces and moments due to viscosity 

 and the stabilizing fins are given in Table 2 and Table 3 of Reference 1. 



EQUATIONS OF MOTION 



If we let a„ = 5„e , a^ = ^^e , the total exciting forces F , and the 

 total pitching moment F^., then, the equations of motion can be expressed 



(M+A„_) a„ + B„„a„ + C-„a- + A„^a_ + B„^ai. + C-^a^ = F_ 



(I+A^^) a^ + B^^a^ + C^^a^ + A^'d^ + B^„a„ + C^_a„ = F_ 

 55 5 55 5 55 5 5J j 5j j 5j j 5 



(96) 



where M is the mass of the ship and I the mass moment of inertia about the y-axis. 

 The hydrostatic coefficients are given by 



S3 = PS V 



C33 = C33 = - Pg[M^-Xg.A^] (97) 



C33 = Pg[lL+A^(Xg-x^)^] + i^-m • A 



24 



