Faltitnsen 
is the time variable. The wave number vy can be written as 
re = (6) 
where 2 is the wave length. The frequency of encounter w is re- 
lated to Os sl and U for the head-sea case by 
n= oe aoe et (7) 
We are going to operate with a slenderness parameter e 
It is a measure of the transverse dimensions of the ship compared 
with the length of the ship. So e€ isa small quantity. If we denote 
the x, y, z-components of the normal n on the wetted surface of 
the ship by n, , n5, ny respectively, then we can set 
Hay TCE “a = Oe mh = Oty (8) 
We will assume that the frequency of the wave has the following 
asymptotic behaviour 
nee (9) 
Using (6) this means that 
Ill THE ZERO-SPEED PROBLEM 
The frequency of encounter, w , is the same as the frequen- 
cy of the waves, wo, for the zero-speed case (see (7) ). The time 
dependence of the incident wave is given by e!“* (see (5) ). It is 
expected that the time dependence for the total potential is also given 
by ¢'¢ t | We will use this fact and now write down the equations to 
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