A New Appraisal of Strip Theory 



1. Develop rigorously the linearized equations of motion. 



2. Use the strip theory technique to compute the values of the coefficients 

 of equation of motion as well as the excitation terms from elementary arguments 

 based on the results of two-dimensional flow theory. 



In fulfilling the latter step, the reason why strip techniques are employed, 

 the assumptions implicit in strip techniques, as well as the upper limit of accu- 

 racy that can be expected from strip techniques will be considered. 



We will start from the basic concepts of the mechanics of rigid bodies fol- 

 lowing Abkowitz [12,25,26]. His approach, similar to those used by aerodynami- 

 cists, provides a concise statement of the kinematical and kinetic problem and 

 readily identifies all of the physical mechanisms involved. After the equations 

 of motion have been developed in an accurate manner, all that remains to be 

 done is to determine the values of the coefficients of the equations as well as 

 the forcing functions. It is here that use will be made of the cross-flow hypoth- 

 esis and two-dimensional hydrodynamic theory. 



The reader may well at this juncture question the consistency of the paper; 

 first an extensive investigation using an existing theory is presented and then 

 the very foundation upon which the theory rests is questioned. This is true. 

 However, it is only after usir^ a certain procedure that one can really appreci- 

 ate and question it. Furthermore, it is suspected that the inconsistencies which 

 seem to exist in the Korvin-Kroukovsky approach will not radically affect the 

 final result. This is probably due to the fortunate cancellation of errors, but 

 this remains to be verified. 



A basic difference between the approach formulated by Korvin-Kroukovsky 

 and the approach proposed in this paper is that hydrodynamics will be employed 

 after dynamics have been utilized. Furthermore no attempt will be made to force 

 fit the mathematical model to conform to experimental results, but rather a ra- 

 tional approach will be developed with the hope that eventually, refined experi- 

 ment will agree with refined theory. 



Derivation of Equations of Motion 



In this section the mathematical model describing the six-degree of freedom 

 motion of a surface ship in regular waves will be developed first and the results 

 will then be specialized for the case of pitching and heaving motions. The fol- 

 lowing assumptions will be made in developing the equations: 



1. The ship will be considered as a rigid body. The high-frequency vibra- 

 tion modes of the hull excited by the low-frequency wave encounters will not be 

 considered here. 



2. The size, geometry, mass and mass distribution of the ship are assumed 

 known and invariant in time. 



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