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