Computatton of Shallow Water Shtp Mottons 
Finally in Section 6 we present computed sway and yaw motions, 
neglecting coupling with roll. This is justifiable, as discussed in 
Section 2, if the metacentric height is sufficient to remove the roll 
resonance period from the range of wave periods of interest, a situa- 
tion which is not unlikely in shallow water. The resulting motions 
agree well with simple approximate and limiting results, which may 
be used for estimates in lieu of the very complicated computation 
procedure needed in the general case. As indicated by Tuck and 
Taylor (1970), the detailed computations are, however, of importance 
if swaying is to be in any way resisted, by moorings, fenders, etc. 
In no case have the present results been experimentally verifi- 
ed. The apparent lack of systematic (as distinct from ad hoc) expe- 
rimental measurements of ship motions in shallow water in the publish- 
ed literature is deplorable in view of the importance of this subject 
today, and it is to be hoped that this situation will be remedied as 
soon as possible. 
II. THE EQUATIONS OF MOTION IN GENERAL 
The equations of motion for any ship moving sinusoidally with 
complex amplitude §; at radian frequency o inthe jth mode of 
motion, the time-dependent displacement being 
a(t) = ipa dieh (2. 1) 
are (Salvesen, Tuck & Faltinsen 1970, Tuck 1970) 
Here Mjj is a generalized mass matrix, i.e. 
Mo 8 0: Mz 
0 M 0 -Mz, 0 Mx, 
He PGR Ne REMe ahd 
i ea 
[M5] OhigaMia AO «Mines WOd <dtnc sae 
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