Beck and Tuck 
damping. Thus, you can see the infinite motion at resonance in both 
pitch and heave, just as you would expect. Finally, the solid lines 
(labelled ''Tuck"') are from the present theory without diffraction ef- 
fects, and the dotted lines are the results of Kim. The differences 
between the two are very interesting because slender body theory is 
a theory which is inherently good for very long wavelengths, and 
strip theory, on the other hand, was developed for a higher frequen- 
cy where the wave length is the order of the beam, What you can see 
in Figures 1 and 2 is that at the low frequency end, Tuck's results 
gave larger motions and at the high frequency end, Kim's results 
are larger. In the region of short wave lengths we would not expect 
our theory to give particularly good results since it was derived for 
very long waves. In this region strip theory would be expected to 
produce the more accurate results. ~ 
Notice that the results in both Figures 1 and 2 are reasonably 
close to the first order theory. This is because of the dominance of 
the hydrostatic terms and the Froude-Krylov exciting force. The 
pitch results for slender body theory do show a marked increase 
over the first-order theory at around L/) of .8. This is due pri- 
marily to the increase in added moment of inertia. We can actually 
see this in Figures 3,4,5 and 6. In addition, the reasons for the 
differences between slender body theory and strip theory can be ob- 
tained from these figures. 
In Figures 3 and 4 are the heave, added mass and damping 
for head seas. In Figures 5 and 6 are the pitch added inertia and 
damping. The solid lines are the results of slender body theory. At 
low frequencies, we can see that the pitch added inertia of slender 
body theory is much higher than computed by strip theory. This ac- 
counts for the larger pitch motion in this region. In the higher fre- 
quency region, the damping of both heave and pitch computed by 
slender body theory are much larger than the strip theory results. 
This accounts for the fact that in this region, where there is reson- 
ance, the motions we compute are much smaller than Kim's, In this 
region Kim's results are no doubt more accurate. 
In the low frequency range, we know that theoretically the 
damping curve has to go to zero with zero slope at zero frequency. 
The slender body theory correctly predicts this, whereas the strip 
theory results, which are not strictly valid in this region, asymptote 
to zero ata slope other than zero. 
In the high frequency region, the heave added mass and pitch 
added inertia as computed by slender body theory go to zero. How- 
ever, we know that they should asymptote to a finite value obtainable 
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