guidance, flight mechanics and trajectory optimization

2.2.4 Impulsive Rendezvons Techniques
-.. - ---I--.-----.
Tn thi.s section, the development of guidance equations in a linear
gravity field will be restricted to determining an impulsive velocity
correction such that a rendezvous till take place at some time in the future.
The techniques of this secti.on can be thought of as defining a reference
trajectory along which the rendezvous vehicle is to travel. Once this
reference trajectory has been established, the actual steering equatinns
(i.e., orientation of the thrust vector as a function of time) can be
determined by the methods discussed in a previous monnqraph of this series
on boost-guidance equations (Reference 2.16). The section below gives a
discussion of two simp3.e techniques for utilizing cal cu!.ated velocity impulses.
Impulsive velocity changes have been considered in detail in the
monograph on mi.dcourse guidance (Reference 2.15) and this reference is
recommended for a more com@ete formulation including the effects of errors
in data and optimization of mu!.ti.ple i.rnpulse schemes.
2.2.4.1 Approximating Velocity Impulses
The use of a model having a linear variation in gravity generates the
necessity of neglecting the effects of finite bnrning time in order that
closed form solutions be obtainable. Al though, th,e use of imp111 sT.ve
ve3 ocity changes is essential to the simoV fication of the equ,ati ons, their
physical realjzation can be only anproximate. If a true impulse could he
achieved, then the guidance mechanization won!d simply be to orient the
thrustor along the direction of the required vel.ocity chanece and apply an
impulse equal to the magnitude of the required chance. Since th.e rocket
motor must bllrn for a finite time (the length of t?me depends upon the
thrust capability in relation to the magnitude of the velocity increment)
the orientation of the required veloci.tg increment will., generally, nnt
be the same at the initiation and termination of the thrusting period.
Thus, if the rocket
v
!ENDEZVOUS
VEHICLE ORBIT
Figure 2.4
Di.rection of Velo&tp Correction
TRAJECTORY
Rocket motors were oriented along the required AV vector and maintained in
that orientation throughout the thrusting period, the resulti.ng velocity
increment wnnld have the correct magnitude, but it would be directly incorrectly.
39