singular Perturbation Problems in Ship Hydrodynamics 



Fig. (Z-4). Two Coordinate Systems for 

 Oscillation Problem 



The absolute velocity of the center of gravity Is: 



- Ui' + ico^jk' = (- U cos ^5 - icolj sin ^5) i 



+ {- U sin ^5+ iw^ cos ^5) k (2-70) 



= - UI + (icoe, - Uejk (2-70') 



•J 5 



where (i,j,k) are unit vectors in the Oxyz system, and (i', j'»k') 

 are unit vectors in the O'x'y'z' system. 



Let the body surface be defined by the equation: 



S(x,y,z) = 0. (2-71) 



Denote the unit vector normal to the surface, inwardly directed, 

 by n : 



n = n^i + n^j + n^k* 



(2-72a) 

 It is convenient to make a number of other definitions , as 



follows; 



1) nj : Extend the above definition of nt to j = 4,5,6 as 

 follows: 



723 



