Motions of Moored Ships in Six Degrees of Freedom 



Similarly, you are dealing with a case of a sine wave here 

 which I do not think is quite apropos, but nevertheless it is an analy- 

 tical exercise that has its utility. How different are the results for 

 the case you have obtained here with the non-linearity included as 

 compared to the linear theory ? There must have been some results. 

 Is there any significant difference ? Does it occur when in a certain 

 region we have certain wave amplitudes ? This will certainly be use- 

 ful to us. 



Similarly, if you have an application to a real condition, even 

 though it is a harbour and has a very narrow tune system, there are 

 swells that come in and you have to treat the problem as one for a 

 random system. There are techniques known as describing functions 

 which you can use, and I am sure you can use them. Your reference 

 says your thesis dealt with this problem area. It would be a natural 

 and wonderful extension of this procedure. The question then is what 

 are the theoretical results and how would they compare with the case 

 of linearity ? 



In concluding, I want to say something that is similar to the 

 statement Dr Saint-Denis made. There is a statement which I used to 

 hear years ago and perhaps it is applicable to my own delivery some- 

 times, but it is of oriental origin. It is essentially that one picture is 

 worth a thousand words. I think we ought to make a little inversion 

 here and put some more words together with some pictures, and the 

 end product comes cut really two years from now. This is a tremen- 

 dous opportunity to make a substantial contribution, and I should 

 greatly like to see it. 



REPLY TO DISCUSSION 



I-Min Yang 



Tetra Teeh 3 Inc. 

 Pasadena, California 3 U.S.A. 



(l) The discusser said, ". . . you just take account of what I consi 



der to be self mode nonlinearities, . . . ". This is not true. It is true 

 that the matrix K is assumed to be diagonal, but if you read this 

 paper carefully, you will find that k. •, are unknown quantities and 

 their determination depends on all six modes of motion. 



683 



