surface. If the depth of water is assumed infinite, the condition of fluid 

 motion at infinity, both horizontal and vertical, is that the fluid 

 velocity due to the disturbance by the ship vanishes, and that the fluid 

 motion is just the sum of the uniform flow and the incident wave. The 

 radiation condition at great distance should be considered as well. If the 

 hull surface at each instant is expressed by the equation 



y = f(x,z,t) (90) 



the boundary condition on the hull surface becomes 



V dx) 3x + dz 3z 3y U ( " yJJ 



Now we consider only the heaving and pitching oscillations because 

 surging motion causes fluid motion of higher order. Designate the vertical 

 displacement of the center of gravity by z and the angle of pitch by ty and 

 take coordinates x , y , z fixed to the ship. Then the relation between 

 the coordinate systems (x,y,z) and (x ,y ,z.) is 



x = x cos ^ - (z-z ) sin ty 



y = y — 



z.= x sin ip + (z-z ) cos ip 



The equation of the hull surface in reference to the moving coordinates 

 (x„,y n ,z„) is independent of time, such as 



y o = f o (x o' z o ) (93) 



It is assumed that z and ty are of the order of 5, and after omitting 

 higher order terms, one can transform the hull boundary condition into the 

 following equation. 



39 



