and Newman and Tuck to solve this problem. Because the unsteady motions are assumed 

 small, the potential (})„ in Equation (3) can be decomposed linearly 



j = 6 



j = l 



where ^ = incoming wave potential 



'4>-j = diffraction potential 



'P. = velocity potential due to motions of the ship with unit amplitude in 

 each of six degrees of freedom 



^, = amplitude of motion in each of six degrees of freedom 

 The diffraction potential, <^-,, satisfies the following condition 



|- ( ^ + (^ ) = for y = h(x,z,t) (18) 



dn o / 



and the velocity potential, ^. (j=l, 2, . . . 6) , satisfies the body boundary conditions 



<^. = -icon. + m. (19) 



Here, the components of the unit vector are defined as 



(n^,n ,n„) = n (20) 



(n^,n^,ng) = (xxn) (21) 



and m. are defined by Ogilvie and Tuck as 



{■a-^,m^,m^) = m = -(n-V) V(t)-|^ (22) 



