VESSEL EQUATIONS OF MOTION 



by 

 Dr. R. Bhattacharyya 

 For the prediction of ship motions the so-called "strip theory" is 



used universally, although there are many versions of this theory depending 



on the problem formulation, the method of solution as well as the inclusion 



of the forward speed effect. 



The original version as given by Korvin-Kroukovsky and Jacob was de- 

 veloped from an engineering point of view and various terms of the equations 

 of motion for heaving and pitching motions were based on somewhat arbitrary 

 defininition of the relative motion between the vessel and the waves. An im- 

 provement of the problem formulation was made by [ 8 ] from intuitive point of 

 view whereas Reference [23] developed a strip theory on the basis of mathema- 

 tically consistent perturbation technique. A major significance of the theoreti- 

 cal methods was the elimination of the original relative motion approach of 

 Korvin-Kroukovsky and instead, as given by Ref [20], the ship motion problem 

 was developed as a sum of radiation and diffraction problems. In other words, 

 the total forces and moments acting on a vessel in a train of regular waves 

 are equal to the sum of the forces and moments acting when the ship is oscillating 

 in calm water, together with the wave forces and moments acting on a restrained 

 vessel. This is quite a significant result, especially from the point of view 

 of model experimentation. 



It should be pointed out, however, that although there are differences in 

 various versions of the strip theory it should not be construed that any one 

 particular version is significantly better than the other, except in some 

 particular cases. 



There are three different methods for the longitudinal motion as given by: 



1) Gerritsma and Beukelman [8] 



2) Ogilvie and Tuck [23] 



3) Salvesen, Tuck and Faltinsen [26] 



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