Boundary conditions which are satisfied by each component on the hull 

 surface are 



3<*>/3n = n , 3^ 2 /3n = n 2> 3</>/3n = n 3 



3¥?,/3n = (y-y G ) n 3 - (z-z Q ) n 2 = n^ 



30 /3n = (z-z G ) n 1 - (x-x G ) n 3 = n 5 



3^ 6 /3n = (x-x G ) n 2 - (y-y G ) n 1 = n^ 



3^ 1 /3n = - 3u/3n = m 1 



3^„/3n = - 3v/3n = m„ 



3ip_/3n = - 3w/3n = m„ 



3^ 4 /3n - - g^ {(y-y G )w-(z-z G )v} = m^ 



3^ 5 /3n = ~ g^ {(z-z G )u-(x-x G )w} = m 5 



3i^ 6 /3n = - -jej- {(x-x G )v-(y-y G )u} = m 6 



(314) 



Forces and moments acting on the hull are expressed by the integral 



•.--{[-, 



p dS 



n = 1, 2, 3 for force 

 n = 4, 5, 6 for moment 



(315) 



Omitting terms of the second order with respect to the oscillation ampli- 

 tude, the fluid pressure is given by 



p - p 



TT 2 Y . U ,„, 1 2 , Y l , Y l , r l , r l 



= U » + ■=— V$_ + -r— + U ■= + V -z + W » 



p 3x 2 ' 0' 3t 3x 3y 3z 



(316) 



where p is the hydrostatic pressure. We divide the above pressure into 

 a part due to U<j> n and that due to cj) such as 



110 



