Motions of Moored Ships in Six Degrees of Freedom 



example, in equation (l), if f(x) is a linear function of x , then equa- 

 tion (l) is always linear. ) Many papers have been published in deter- 

 mining hydrodynamic coefficients and wave forces and since the main 

 purpose of this paper is to present an approach to solve the nonlinear, 

 asymmetrical problem due to the presence of mooring lines, I did 

 not even try to explain how to find these coefficients in this paper. 



The explanation of the approach is quite complete. If one reads 

 this paper carefully, he will find that, although it is a quite short 

 paper, it contains all information about the approach. 



It is true as the discusser pointed out I failed to compare the 

 results with measured data. However, the comparison with an exact 

 solution does indicate how good the approach is. If the hydrodynamic 

 coefficients and the representation of mooring lines are adequate, 

 then this approach will give very reasonable and practical results. 



DISCUSSION 



Paul Kaplan 



Oceanics Inc. 

 New-York, U.S.A. 



My comments are somewhat similar to those of Dr Saint-Denis 

 but perhaps they are motivated by different reasons. In some ways, 

 when I looked at the paper and considered the content of it I was re- 

 minded of a modern song that was popular a couple of years ago by 

 Miss Peggy Lee. It is called "Is that all there is". If you think about 

 the song, it starts out on a sad tone and that is the way I felt initially, 

 but the song proceeds by careful consideration to some sort of posi- 

 tive outlook. Perhaps if you bear with me and my discussion and some 

 interchange between the author and myself, the same result may be 

 achieved. 



My interest in this particular subject is indicated by the fact 

 that there is a reference to the paper I wrote ten years ago dealing 

 with the motions of a moored ship with six degrees of freedom, and it 

 was linear. Two years ago at the last Naval Hydrodynamics Symposium 

 I presented a similar subject which was just concerned with a few pro- 

 blems in the whole general area of mooring and positioning ships at 



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