guidance, flight mechanics and trajectory optimization

The solution to these equations are
I (2.13)
From these equations, it is seen that the position and velocity will simultaneously
go to zero if k < 1. However, if the acceleration is examined,
it will be found that for $ 4 k < 1 infinite acceleration is required
as t -c f/4 . Therefore, for practical rendezvous, k must be restricted to
the range 0 4 k c 3.
Flight control is accomplished by generating an error signal, V,, from
the continuous monitoring of the actual and desired velocity
and igniting the rocket motor whenever this value reaches a specified thres-
hold. The thrust angle (i.e., the angle between the thrust vector and the
x axis) is
e=ay:cbo
Figure 2.6
In-Plane Steering Angle
The relative out of plane motion (i,) is sinusoidal and uncoupled from the
planar motion. Thus, the-out of plane motion could be nulled separately;
alternately, the desired Z can be selected as some function of the Z error,
e-&J
2, = -az
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