For the lateral motions three different approaches are given by: 



1) Kaplan, Sargent and Raff [15] 



2) Salvesen, Tuck and Faltinsen [26] 



3) Grim and Schenzle [12] 



Of all the methods above only Ogilvie and Tuck, and Salvesen et al satisfy 

 the Timman -Newman symmetry condition. 



Based on two-dimensional case, there are three different ways for the 

 numerical calculation of fluid reactive forces and moments , i.e., added mass 

 or added mass moment of inertia and wave damping. 



1) The first and the simplest method is the use of conforraal mapping 

 techniques with no-free-surface effects. Apart from the classical 

 extended Joukowski transformation method of [17 ] which was improved 

 by [ 1^ whereas both [ Al ] and [14 ] applied the Schwarz - Christof fel 

 transformation in obtaining the added mass. 

 3) Another method is the use of source distribution over the hull 

 surface which can also be attributed to [35 ] . The practical use 

 of the source distribution method is due to [ 7 ] which is often 

 referred to as "Frank Close fit" method. 

 As mentioned above, the fluid reactive forces and moments are generally 

 known as added mass/moments of inertia and damping because they act in phase 

 with the acceleration and the velocity of ship motion, respectively. Presently 

 there are four methods available for practical calculation: 



1) Infinite frequency approach (no free-surface effect) [16 ] 



2) Lewis transformation [ 9 ] 



3) Tasia close-fit mapping method [ 33| 



4) Frank close-fit source distribution method [7] 



56 



