Computing Hearing and Pitching Motions 489 
1.0 
B=06 
2.2 
1.8 
1.4 
12 
=< 10 
SS 08 
SVQ 
6 
j 
an 
YON 
| ONTOS SS PSS I 
2.2 
18 
1.4 
1.2 
1.0 
-05 
08 
0.6 
-1.0 
04 
H= 02 
OM ON O4Ie = OCR SOM wanes 
HEEB: 
2 
Fig. 2. Heaving motion; plot of force R for B= 0.6 
Therefore, in the statical case, i.e., a =0, R equals 1. For a periodical heaving 
motion, viz., 
z=Z eit (14) 
fo) fo) 
the force which is required to generate the heaving motion is 
RigiBeZ: e7 2, (15) 
This force is identical with 
Cnt) Czar Ni) 2 + Bz. (16) 
This form is known to be the one side of the equation of motion. It contains: the hy- 
drodynamic force m"z,+ NZ,, the hydrostatic force 5Bz,, and the inertial force mz,. 
A,7/B is the coefficient of the first term in (2) in nondimensional representation 
