Beek and Tuck 
362 + 
%-y 52+ 1/206, as at a 
(5. 6) 
i.e Paeeee : 
and we have s 9 
a $4 = he, ( x ) + S(x ) (5.7) 
H 
Thus finally 
: Q 
A = -po | dx [p65 () + s(x) 
ms 
y 
= -po nf dx Ad, (x) - ¢M (5. 8) 
a | 
where 
y 
M = 2a dxS( x ) (5. 9) 
us)! 
is the mass of the ship. Note that the term involving the mass M 
was erroneously omitted by Tuck (1970). The new result indicates 
that the virtual or total inertia, not just the added inertia, is propor- 
tional to the real part of the exciting force integral (5.1) at B=0. 
The above analysis may now be repeated for T,;:, for all 
i,j = 2,4,6 except for the roll self-force term T44 * — example 
z J 2 v 
Tg = Teo = pba dxxA¢, (x) -po I, dxxS(x) (5. 10) 
ee oe ‘| docx" A@, (x) Sig I, at s(x) (5. 11) 
A i 
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