guidance, flight mechanics and trajectory optimization

The fundamental matrix for A can be written at once as
10 0 0 .O 0
8 1 0 0 0 0
0 0 cos 8 Sin 8 0 0
F(0) = 1 0 0 -Sin 8 cos 0 0 0
for which the inverse is
0 0 0 0 cos 8 Sin 8
0 0 0 0 -Sin 8 cos 0
F-‘(e) = F(4)
The solutions to the equations can now be written in the form
In this case, the matrix G(0 - Go) = F(B) FD1(Qo) is easily seen to be
-
1.60
1.61
GM-8,) = F&J-q) 1.62
Note that F(Oj = F-l(e) = I. In fact, since no loss of generality occurs
by choosing 0, = 0, this value will be assumed for the remainder of this
section. The six integrals in the solution for w (0) (called "Z"> will be:
2, =
s
0
8
u2 d-r
e
I- =
J
(73 f32y)d7-
0
1.63