guidance, flight mechanics and trajectory optimization
guidance, flight mechanics and trajectory optimization
guidance, flight mechanics and trajectory optimization
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2.2.4 Impulsive Rendezvons Techniques<br />
-.. - ---I--.-----.<br />
Tn thi.s section, the development of <strong>guidance</strong> equations in a linear<br />
gravity field will be restricted to determining an impulsive velocity<br />
correction such that a rendezvous till take place at some time in the future.<br />
The techniques of this secti.on can be thought of as defining a reference<br />
<strong>trajectory</strong> along which the rendezvous vehicle is to travel. Once this<br />
reference <strong>trajectory</strong> has been established, the actual steering equatinns<br />
(i.e., orientation of the thrust vector as a function of time) can be<br />
determined by the methods discussed in a previous monnqraph of this series<br />
on boost-<strong>guidance</strong> equations (Reference 2.16). The section below gives a<br />
discussion of two simp3.e techniques for utilizing cal cu!.ated velocity impulses.<br />
Impulsive velocity changes have been considered in detail in the<br />
monograph on mi.dcourse <strong>guidance</strong> (Reference 2.15) <strong>and</strong> this reference is<br />
recommended for a more com@ete formulation including the effects of errors<br />
in data <strong>and</strong> <strong>optimization</strong> of mu!.ti.ple i.rnpulse schemes.<br />
2.2.4.1 Approximating Velocity Impulses<br />
The use of a model having a linear variation in gravity generates the<br />
necessity of neglecting the effects of finite bnrning time in order that<br />
closed form solutions be obtainable. Al though, th,e use of imp111 sT.ve<br />
ve3 ocity changes is essential to the simoV fication of the equ,ati ons, their<br />
physical realjzation can be only anproximate. If a true impulse could he<br />
achieved, then the <strong>guidance</strong> mechanization won!d simply be to orient the<br />
thrustor along the direction of the required vel.ocity chanece <strong>and</strong> apply an<br />
impulse equal to the magnitude of the required chance. Since th.e rocket<br />
motor must bllrn for a finite time (the length of t?me depends upon the<br />
thrust capability in relation to the magnitude of the velocity increment)<br />
the orientation of the required veloci.tg increment will., generally, nnt<br />
be the same at the initiation <strong>and</strong> termination of the thrusting period.<br />
Thus, if the rocket<br />
v<br />
!ENDEZVOUS<br />
VEHICLE ORBIT<br />
Figure 2.4<br />
Di.rection of Velo&tp Correction<br />
TRAJECTORY<br />
Rocket motors were oriented along the required AV vector <strong>and</strong> maintained in<br />
that orientation throughout the thrusting period, the resulti.ng velocity<br />
increment wnnld have the correct magnitude, but it would be directly incorrectly.<br />
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