Beck and Tuck 
III. COUPLED SURGE, HEAVE AND PITCH MOTIONS 
The formulae for the transfer functions Tay 5 T53 were de- 
rived by Tuck (1970), and ina similar manner we may obtain the fol- 
lowing results, >validtior all yie= 4, 3:75, and-all) i= 173,585 
p 
Mis nc ero / dxe ee (x) (3. 1) 
4 
T gia amt Bald. cohhe At Oy (k 
i wee pe pet py es ap eat Jx- §]) » 
(3.2) 
where 
A(x) = )'S"{ 268) (3. 3) 
A,( x). 2 Bee) PE 
A,( x ) = -xB(x) zi yiey (3.5) 
AL a 4 | -B60 Fi = B- Steal) cos B (3. 6) 
Here B(x) is the full waterline width and S(x) the section area at 
station x, while ie is an Hankel function (Abramowitz and Stegun 
1964, p. 358). 
A brief derivation of the above results is given in Appendix I. 
The physical plausibility of these results, especially the rather com- 
plicated formula (3.6) for the diffraction exciting force, may be ex- 
hibited by considering the direct effect on the equations of motion, 
For instance, in heave, i= 3, the equations of motion (2.2) 
state 
2 
-o MS, + C4 8, + Cy. S5 - T35 Sg = 13, 5) + Tey $3 * M35 55 * 157% 
f 2 
_ tae ikEcosB 
=f J ne if dé[B(E) (f,- 85 5-S5¢ (3. 8) 
1552 
