Kaplan, Sargent and Goodman 
determine whether they had any influence or could be discarded for 
further consideration. It was suspected that these terms would have 
little effect, based on the fact that the heave motion is primarily 
influenced by pressure effects and the only hydrodynamic or hydro- 
static terms that would influence the heave motion would be those 
terms involving heave motions per se. Previous simulation studies 
of similar. SES craft have demonstrated that the coupling of pitch 
motion into heave had little effect, and the results obtained for heave 
motion responses with these pitch derivative terms deleted were 
almost the same as when they were included. Thus they were neglec- 
ted in the identification experiments. 
A similar treatment in the case of pitch motion was made 
where the 4 pitch stability derivatives associated with Equation 
(41) were estimated. Computations made with all motions (9, 06, 
z and z) assumed to be measured and available produced values 
for these particular derivatives, with different magnitudes resulting 
for the coupling coefficients M, and M; that could not be recon- 
ciled with simple estimates based on hydrostatic computations, for 
example, in the case of the derivative Mz. Similarly the change in 
sign of M; in different runs also indicated that this particular 
variable had a small influence on the resulting pitch motion, and in 
accordance with the procedure applied in the case of heave motion 
these quantities were also neglected. The results obtained for the 
derivatives Mg and Mg , with all motions measured including the 
effect of M; and M,, are shown in Figure 4, while those obtained 
with the assumption that M, = Mz; = 0,are shown in Figure 5, 
which uses only measurements of g and @ . These results are suf- 
ficiently close so that it can be assumed that there is no significant 
influence of these variables, just as in the case of the coupling coef- 
ficients for heave motion, and hence they can be ignored in future 
system identification work. 
An interesting result was obtained when it was assumed 
that only measurements of the pitch angle were available, and in that 
case the stability derivatives are shown in Figure 6, which indicates 
a well converged solution that does not deviate much from the initial 
guess values. In order to determine if these coefficients are really 
appropriate to this particular motion, the pitch angle trajectory is 
shown in Figure 7, together with the estimated trajectory using these 
values, It is seen that very good tracking of the observed pitch tra- 
jectory is indicated by these values and hence they can be used as 
the appropriate estimates from system identification, This is in- 
dicated by a comparison of values given in Figure 6 with those in 
Figures 4 and 5, showing only a small difference in M g while there 
is some difference of the order of 25-30% for the derivative M6 3 
1656 
