440 Alex Goodman 
and 
b 
- a 2 sin =| (2 ot‘) [ sin (.t - =| 
= & sin a (45) - [cos (ut = 3) + M, (B23) 
where /,,, and (Mg), refer to the model moment of inertia and metacentric stability, respec- 
tively. 
As for the heaving case, in-phase and quadrature components of force and moment can 
be written as: 
P 
(Z,) + (2), = ow? 2 sin a Zz. (B24) 
in 
J BE as Cally wpe 
(21) ut v (29) out oS a (2: Boat = (3 pt Zo 
A n, (B25) 
p 
2 
‘ are (21), | a wo? (22 sin ) Gln) = Mom {2 sin =) = 
x (25), = Cie = -wU (22 sin ) (5 0¢'m,) (B27) 
The pitching rotary and acceleration derivatives, written in nondimensional form, can be 
expressed as: 
nS a2... + (24'), |] — 
CBOs pee se k R71 one / (22') oud (B29 
qa m = 3q ' 
(Hy) m 
k22"),. . Cay, 5 ee? (B30) 
x ly 
4 8q_' aw 
