guidance, flight mechanics and trajectory optimization

equations in the set with a, b and c set equal to zero. This guess for tf
and d', is next substituted in the three equations:
and this set is solved for a, b, and c. Substitution of these values of a,
b, and c in the equation for y(tf) will generally not result in it being
zero, so further iteration (on time) is made. The time increment is chosen
by seeking an increment which causes the remainder from $(t g ) to change sign.
Half this interval is then used to recompute a, b, c and su sequently y(tf).
This process is then continued until the remainder from y(tf) becomes
acceptably small.
The authors of Reference (4.18) investigated three forms for f(t) in
Equations (1.21). These forms were: (1) t2, (2) //(ttd), and (3)&t .
Of these three, only the quadratic one proved unacceptable because of the
inability to maintain the small angle approximations. The other two forms
were found to be stable at all points on the trajectory, and the trajectories
obtained were very close to the optimum trajectories as determined in
Section (2.4.1).
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