F^ = -P 



JJ (ia.n.4^.) V V^^k^ 



k=l 



dS e 



-iojt 



(83) 



ADDED MASS AND DAMPING 



We write the integral of the term under the summation in Equation (83) as 



where 



'i =27^3 



^u e 



-icot 



k ^k 



(84) 



k=l 



t ,, = - p II (iojn.+m. ) [c 

 Jk "^ JJ 2 3 



^^+<^^+C^{K)(c^^+<t>^)] dS 



(85) 



The terms inside the bracket represent the unsteady potential ^ which results from 

 oscillation. Equation (85) denotes the hydrodynamic force and moment in the j 

 direction per unit oscillatory displacement in the k mode. 

 The added mass and damping are defined by 



t., = - A., 0) 

 Jk jk 



i B., a 



(86) 



where A., is added mass and B., is damping. Both A., and B., for 1=3 and 5 and 

 jk jk '^ ^ jk jk -J 



k = 3 and 5 are given in Table 1. In Table 1, is used the following notation: 



^3 = *R + i^j 

 *3 = \ + ^*I 



S = Sr + ^Si 

 S = Sr + ^Si 



^ = -(Un3+xm3); ^5 = "t^ ^3 " ^<^^ 



19 



