Murthy 



Water elevation 



y i L ► n \ ™ V i ff t k T m n „ , , 



S (x, y;t;5,0,a, e) = Re Z-, e 5/3a e S,. (x, y) 



k, 1, m, n 



klmn 



Surge displacement 



x(t;6;/3;a) = Re L e 5 a 

 k, 1, m 



icrt k 1 m _ 

 x 



klm 



Heave displacement 



- / i „ V iO"t k 1 



z (t;6;p;a) = ReLe 5 /3a 



iat k„l m _ 

 z. 



k, 1, m 



klm 



Pitch displacement 



6 (t;«;|8;a.) = Re X) ' 



e 

 k, 1, m 



klm . 

 8 0a 9 



klm 



(2-2) 



The frequency o" is that of forced oscillation in calm water 

 or equal to the encountered frequency cr e of the waves in a regular 

 seaway. The displacement parameters are not expanded in powers 

 of e for, by definition, a is the order of the displacement due 

 wave excitation of the order of forced displacements in the absence 

 of waves. The quantities relating to the motion of the water contain, 

 however, all the four parameters. A phase lag between the displace- 

 ments is not explicitly shown in the above expressions. However, 

 if for example, z and 9 are considered as complex quantities 



a phase lag is implicit between heave and pitch. 



The steady displacements of the type 



110 



110 



and 



110 



relate to motion in calm water and the oscillatory displacements 



and 9, 



*kl, 



klm 



klm 



are restricted to the first order in a , i. e. with m = 1 since we 

 shall be evaluating forces and moments up to a maximum order of 



bfiad and /3 2 are and for this purpose displacement of the first 



S 2 at 



122 



