Beek and Tuck 
and 
z ; ' re 
%, V (y +¥,) V4 (5.17) 
from which follows * 
Ag, = ZC ve - 1) (5. 18) 
and 
Ady KAZE; (Miguel jap-Gs). (5. 19) 
Thus we have the integro-differential equations 
AP; (x) Cc, (x) 
L 
t Zz 
alg ie forsee 0 Ole 8) zeta (5:20 
which can be converted into integral equations of the form 
5 od 
i (1) l Aelt) wa 
A [ere (k |x- El) “e| dé 26, (E) sin k(x - ) 
0 
ce) (5.21) 
= A. cos kx + B. sin kx Ao dé ——> G c 6) sink(x-&) . 
where A; , B; are constants to be determined by the end conditions 
Ad.(+ L) = 0. Although the left side of (5.21) contains the same 
kernel for i= 4 asfor i=2, the parameter C,(x) which appears 
on the right has not yet been evaluated numerically, so that in the 
following section results are given only for sway and yaw. 
VI. COUPLED SWAY AND YAW 
As discussed in Section l., there are indications that rollis 
not a significant mode of motion in shallow water, and that in particu- 
lar its coupling with sway and yaw is small. Therefore we present 
here computed free motions of the Series 60, block 0.80, ship in 
* The quantity C, corresponds to C(x) as in Tuck (1970). 
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