guidance, flight mechanics and trajectory optimization

endezvous velocity requirements from a much wider range of initial con-
ditions than any of the methods discussed previously.
In order to use the two-body equations of motion to determine the
required velocity a time at which rendezvous is to occur must be selected.
Some criteria for selecting the rendezvous.time, r , have been given in
Sections 2.2.3.2 and 2.2.3.4. For the purpose of illustrating the method,
it is assumed that the time till rendezvous is determined from some range
range-rate function, i.e.,
.
G = f’(r) (2.16)
as in Section 2.2.3.4. The procedure is (1) measure the relative range;
(2) determine the desired range-rate ( 6 ) from Equation (2.16), (3)
calculate the time of rendezvous, r , as
R
r= y-
rd
where Pm = measured range
.
5 = desired range rate
(4) determine the position of the target at r using two-body equations
and knowledge the target orbit (5) compute the required velocity by solving
Lambert's problem using the position of the.target at r , the position of
the rendezvous vehicle at t = 0 and the desired flight time r .
TARGET ORBIT REmEzVOUS KEKICLE
ELEMENTS 1 POSITION AT t = 0 1
1
A
1
CALCULATE
POSITION
OF TARGET
----I
;T TTM-5’ =
Block Diagram of Conic RendezGous Calculation
Figure. 2.11
REQUIRED
VELOCITY
If the position and velocity of the target vehicle are expressed in an
inertial coordinate system whose origin is at the center of attraction, then
the position at time T can be calculated from the following (sequential)
set of equations
r= x't
f
'tz
2