to speak about a ''singularity theory" as distinct from a "rigorous theory" based on a 

 more exact solution of the boundary value problem. 



Beside the work of Havelock [18] we mention the well-known investigation by 

 Ursell [19] on the heaving of a cylinder, as an example of a rigorous procedure which 

 becomes indispensable when added masses, the magnitudes of which depend upon the 

 flow field in the neighborhood of the body, are investigated. 



The determination of the ship behavior in a seaway as a boundary-value problem 

 was formulated in its full generality first by F. John, whose papers on the motion of 

 floating bodies [20] are already classical. It is impressive that this investigation led 

 immediately to important practical results in a special case, thus defying classification 

 as only a mathematical exercise. 



Stoker and Peters [21] attacked the explicit solution of the boundary problem 

 in a more general way, restricting it, however, to symmetric motions of the "Michell" 

 (thin) ship. From a methodological point of view this work produced important 

 progress, which is enhanced by a study [22] dealing with the "Stoker-Peters" problem 

 on arbitrary heading angles. It has been pointed out by the present writer that the 

 results achieved by these authors in their first paper indicate that the Michell ship 

 cannot be considered as an adequate mechanical model of an actual ship as far as 

 heaving and pitching motions are concerned. However, quite recently Stoker and 

 Peters have obtained farther rearching results in the case of the general problem [23]. 

 Although explicit solutions apparently can be worked out only with great difficulties, 

 their method represents the ideal goal aimed at in our field of research, since it derives 

 the motion of the ship from the pressure forces on its hull. 



In the case of plane motions, methods of solving the boundary problem have 

 been established by Ursell and Grim [24]. The results obtained represent already an 

 indispensable part of useful knowledge in our field. 



A significant present trend is to treat problems as two dimensional and to solve 

 them as rigorously as possible, although solutions for the three-dimensional potential 

 of pulsating and advancing singularities are known. A strip model is then applied. 

 Because of the inherent limitations of the plane-motion concept it is expected that this 

 trend may be changed rather soon, although Haskind, in an interesting recent paper [25], 

 takes advantage of the simpler procedures used in the two-dimensional case, and at the 

 same time gets rid, as far as possible, of their shortcomings. 



Having given what is thought due credit to strategists of a rigorous approach, 

 we must still pay attention to problems whose treatment by rigorous methods may still 

 prove impossibly cumbersome. An important example is the problem of hydrodynamic 

 impacts associated with the emergence and reentry of parts of the hull, especially of 

 the bottom from and into the water [26]. 



Unfortunately, we have not been able to deal adequately with the resistance 

 problem in this paper. This is partly due to the unsatisfactory status of knowledge in 

 this field, and partly to our inability to obtain literature on valuable work by Japanese 

 researchers, in time for this writing. Research conducted at the present writer's institute 

 at a simplified level has so far led to promising, but not yet conclusive results."* 



3. More Detailed Survey of Problems Connected with Ship Behavior 



The brief sketch of the scientific status in our field leads to the conclusion that 

 beside the promising first efforts to establish a general rigorous theory we have still 

 essentially to rely, probably for a long time, on partial solutions of our problem, resting 

 to a large extent upon inductive and rather intuitive methods. We shall therefore discuss 

 in more detail results obtained by the latter approach. 



** Reference is made to recent publications by Hanaoka and Maruo. 



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