the linearization of boundary conditions at the free surface. In the case 

 of ships or other floating bodies making oscillations on the free surface 

 with its average position at a fixed point, indicating no average veloc- 

 ity, the boundary condition at the free surface can be linearized in a 

 simple fashion by assuming that the amplitude of the oscillation is 

 sufficiently small. Therefore, no restriction is imposed on the shape of 

 the body. By the employment of the numerical method, one can calculate 

 hydrodynamic forces on any kind of shapes of floating bodies in principle, 

 and it is known that some numerical results show fairly good agreement with 

 measured values. However, a rational development of the linearized 

 theory becomes too intricate when the steady forward speed is introduced 



to the oscillating ships. The difficulty in finding a rational solution 



21 

 which is not trivial was first demonstrated by Peters and Stoker. They 



showed that the hydrodynamic reactions such as the added mass and damping 



did not appear in the order of approximation of the linearized theory for 



a thin ship oscillating in the plane of symmetry. There had been extensive 



22 23 



works by Haskind and Hanaoka about thin ships in longitudinal os- 

 cillations in still water before that time. A full condemnation of these 

 achievements by the reason of inconsistency may be unfair, because the 

 consistent structure of theory breaks down on account of just a single 

 reason of the inclusion of the steady forward speed. If the steady 

 forward motion is introduced to the oscillating ship, the possibility of 

 linearization depends on the hull shape parameter as well. The main 

 difficulty in the oscillating thin ship with forward speed lies in the 

 fact that the disturbance generated by the periodical motion of the ship 

 is weaker than the disturbance due to the forward motion. Consequently, 

 the first order theory would lead to an unrealistic conclusion that no 



damping to the oscillation could exist. In order to overcome this 



24 

 difficulty, Newman employed two independent parameters, one of which is 



the oscillation amplitude and the other is the hull shape parameter, namely 



the beam-to-length ratio of the ship. Although the justification of the 



damping and added mass of the thin ship is attained by the use of two 



parameters, more serious difficulty appears when the ship is moving in 



36 



