Computatton of Shallow Water Shtp Mottons 
sway and yaw, with complete neglect of roll coupling. The equations 
to be solved can be written 
-T> 'S - thé vy = F, (6. 1) 
is Ra ae i eee ae one) 
where 
; 0 
es = -po h | dx Ad., (x) (6. 3) 
Lf 
* * 2 
ee ee ea er (6. 4) 
f 
¢ ikpgh sin@ i dx Aq, (x) SPH SOAs, alig G) 
by 
I 
2 0 
y 
6 Cyike gh sin of dxx Ao, (x) ois SoBe | (6. 7) 
hy 
i 
Here starred quantities represent natural inertia plus hydrodynamic 
effects. Note that natural inertia cancels out corresponding terms in 
the equations (5.8), (5.10) for the unstarred quantities Dam. su lies 
and To, , assuming the unexcited ship is in equilibrium. However 
there is a contribution to T,~ if the longitudinal radius of gyration 
of the displacement of the ship does not equal that of its actual mass 
distribution, expressed in (6.5) as W(x) per unit length. This extra 
term in (6.5) is quite small in practice, but has been included in the 
computed results. 
The quantity Ag.(x) is obtained numerically by solving the 
integral equation (5.21), which for i=2 reduces to 
1565 
