guidance, flight mechanics and trajectory optimization

Fixed Range: Range-Rate Schedule
Range (N. Mi.) Desired Range Rate (fps)
5
-100
1.5. -20
.25 -5
Sears and Filleman'in Reference (2.10)' chose a desired range rate pro-
portional to the square root of the range. Many other range range-rate
schedules could be used and the choice of a particular one could be based on
factors such as (1) the maximum relative velocity expected at the beginning
of the rendezvous maneuvers (2) the type and capabilities of the propulsion
system to be used in the maneuver (3) data acquisition and processing re-
quirements and (4) back-up guidance requirements.
2.2.4.5 Second Order Improvement
If the required rendezvous velocitv is calculated from Equation (2.11),
then the miss at the target (i.e., the difference between the target and
rendezvo!JS vehic!.e) at the time rendezvous is to occur wil! be zero to f?.rst
order. However, if
selected rendezvous
the inin.tia! seFarati.or distance
time is large, the actual target
is lar,ge or if the
miss map be significant!.p
greater than zero.
,$st due to model errnrs. In these cases, an on-board
s&em based exclnsive7y on the linear eqllatinn must inclllde midcnurse
cnrrectio-s f.n achieve reasnqahle miss distances. An alternative is to
use equations of motion which have increased accllracy hecallse nf the
inclllsion of second nrder terms in the expansion of the cnordinates. 33 cl'
eqlTatinns have bee? develnoed in Sect!or 2.7.5 and are of the form
(2.14)
where E(T) is the relative position vector (to second order in the
coordinates) for target orbits of small eccentricity. The vector 0~~ has
components Aiy Biy Ci which are in general non-linear functions of the
initial position and velocity. (See Section 2.1.5 for the exact expressions
for Aiy Biy and Ci ). One way to improve the miss at the target would be to
calculate the requ&ed initial velocities from Equation (2.14). This step
cannot be accomplished directly, however, because of the non-linear nature
of the a; ; thus, appeal to numerical methods must be made. An alternative
to a numerical solution is developed by Anthony and Sasaki (Reference 1.2)
which assumes a solution as a sum of the linear solution plus an error term.
k (0) = /g; (0) + c
46
(2.15)