T = 



= 0. 



57721. 



X 







S,n,? 





h 







o . 







♦(■ 



.3 



_=<^ 2 



q Three-dimensional source strength 



S Area of immersed cross section 



U (-U,0,0) Steady forward velocity vector 



x,y,z Spatial coordinates 



a Multipole strength 



m 



3 Heading angle of incoming wave with respect to the x axis (3 



0° is the following wave, and 3 = 180° is the head wave) 



Euler's constant 



Length of incoming wave 



Spatial coordinates 



Complex amplitude of ship motion 



Two-dimensional source strength 



Total velocity potential 



<J). Velocity potential due to steady forward motion (i=l) or to 



unsteady oscillations (i=2) 



<j>., j = 3,5 Two-dimensional velocity potential for heave (j=3) or pitch 

 ~* (j=5) due to harmonic motion 



<j>., j = 3,5 Two-dimensional velocity potential for heave (j=3) or pitch 

 - 1 (j = 5) due to steady forward motion 



gj Encounter frequency 



0) Frequency of incoming wave 



o 



(n Incoming wave potential 



ip. (j=l,2, . . . ,6) Velocity potential due to motion of the ship with unit 

 - 1 amplitude in each of six degrees of freedom 



(p Diffraction potential 



vii 



