guidance, flight mechanics and trajectory optimization

Another example of proportional guidance is given by Green (Reference 2.17).
A discussion of this method, call logarithmic guidance, is presented here
since a comparison between this type of guidance and an optimum guidance
technique is made in Section 2.3. In this method, the vehicle control
system attempts to adjust the thrust so that the equations below are
satisfied
= /cz $
where Kl and K2 are constants. These equations may be integrated to
illustrate the logarithmic behavior
'The first equation may be integrated
and differential yielding
Thus, the time to achieve rendezvous can be determined as
From these equations, the following bounds on Kl can be determined
k, 4 I (to achieve rendezvous in a finite time)
k, 2 b (to keep p L O" as ,O approaches zero)
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