guidance, flight mechanics and trajectory optimization

Using this notation, Eq. (2.4.3) can be rewritten as
Rho, yo’ = M/y 1
Y
f(;u,, y. , y;)AX +g ~(.q,~~x4~J, f(;~lii;o~,(2-4-6)
L” I
I..& Q(z,,, fil b e the minimum value of the summation xi, j&d, f/‘(&i))AX
where the arguments X, and jf, , again denote the starti&point of the
Note from the grid size in Sketch (2.4.2) and Eqs. (2.4.4) to (2.4.5) that
Y,=/ {y,-%+A%-o+/]but that
the optimal curve connecting
Y, can take any value from 0 to 10. Suppose
the points(x,,#,) and (~$,)r/) has been calculated
and the functionR(z,,y,)
using the Principle of Optimality
to the right) allows the optimalevaluated
for&=/ and # =o,/,z,...,/o.
and the &rid (which is partially
Then,
shown
solution to the original problem
(namely the value of R(xor yo)
to be located.
30
and
Again letting
fi =+ ffi'dp
it follows that Rt~~,p) is given by
P . \
2.6
I.0
0'
Sketch (2.4.3)
That is, the slopeb(,/ at the point (X,,f,/,, would be selected so that the
sum of the two terms !?'cr,,y,, $)A)L + RJZ, ,p) is a minimum where $ =Y,+$'A%.
This is exactly the computational procedure which was followed in the example
problems of the preceding sections.
Equation (2.4.8) can be developed directly from Eq. (2.4.6) by noting
that the operation miy means the minimization is to be performed over all
slopes & with i running from Oto 9. Thus,
M/A/ 5 M/A/
Y' y:* (i-0,9)
Now, substituting this expression into (2.4.6) provides
1 9
63
(2.4.7)
(2.4.8)