guidance, flight mechanics and trajectory optimization

Now, the,magnitude of the required velocity, V, can be determined from the
energy equation
This magnitude- can be associated with a velocity component normal to the
radius (V,) which is found from the conservation of angular momentum
x =pz
and a radial component (V ) found from
Finally, the required velocity vector can be written as
r (0)
-R V -y - r(0)
+v (GX!p_r,
* I(J x r$xql
A variation of this procedure called 'miss distance guidance' and is
described by Gunckel in Reference 2.8. In this method, both the target and
rendezvous vehicle orbits are integrated forward to the rendezvous time.
The difference in their positions, at this time, is the -miss distance. The
velocity required for rendezvous is then found by operating on the miss
distance with the transition matrix.
where
s_v = pJ ( c (Tl) - c ( 7))
VR = velocity vector required of the
rendezvous vehicle at t = 0
yto1 = velocity of the rendezvous vehicle at t = 0
= transition matrix relative variations in
position at t = T to velocity at t = 0
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