Beck and Tuck 
HEAVE-PITCH, 0(1) motion 
Important Forces, 0O(€) : hydrostatics, F-K exciting force. 
Small Forces, O(e ) : added inertia and damping, 
coupling from surge, diffraction 
exciting force. 
3 
Very Small Forces, O(e ) : natural inertia. 
-1 
SWAY-YAW, 0(€ ) motion 
2 
Important Forces, O(e ) : natural inertia, added inertia and 
damping, F-K and diffraction 
exciting forces, 
Very Small Forces, O(e) : coupling from roll. 
ROLL, 0(1) motion 
3 
Important Forces, O(e ) : hydrostatics, coupling from sway 
and yaw, F-K and diffraction ex- 
citing forces. 
Very Small Forces, 0(e°) : natural inertia, added inertia and 
damping. 
Several features of the above table are at first sight surpris- 
ing. Firstly we should note that the conclusion that surge, sway and 
yaw involve large 0(€71) motions, while heave and pitch involves 
only 0(1) motions (i.e. of the order of the wave amplitude) is rea- 
sonable, in that the ship moves more or less as does a water particle 
and the horizontal particle motions in a shallow water wave are much 
greater by a factor of order wavelength/water depth than the vertical 
particle motions. Rollis rather special, and its 0(1) magnitude is 
due to the assumed sufficiently large order of the metacentric height. 
Forced surging is an extremely inefficient method of creating 
hydrodynamic disturbance, so that all hydrodynamic effects on surge 
are small. Note however, that the added inertia is only one order of 
magnitude smaller than the natural inertia, whereas in infinite depth 
it becomes two orders of magnitude smaller. 
Heave, pitch and roll are the only modes to involve hydrosta- 
tics, and the hydrostatic contribution is necessarily dominant for these 
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