guidance, flight mechanics and trajectory optimization

The first area of work to be discussed concerns the optimization of
rendezvous using stepwise thrusting either as a series of impulsive thrusts
or as a series of finite burns separated by coasting arcs. This technique
actually results from a development of switching functions from the
Pontryagin maximum principle. In this second and third portions of the
section, rendezvous studies involving continuous thrust are described. These
sections deal (for the most part) with the final phase of the rendezvous
maneuver; that is to say, the two objects are on the verge of a very near
collision and the engine is to be used with a single burn to alter this
situation and produce rendezvous. In this area of study, field free
equations are, in general, satisfactory and most work deals with such motion.
There is an area of 1 ow thrust rendezvolls studies in which power !.imited
engines are considered. me cost functions for the fuel for such engines is
quadratic, thus the linear differential. eqllations of motion yield a set of
equations for the optimllm sitllat!on which is 1 inear and conseqllentlp so3vabl.e.
Applications of this apnroach have been largely for interp!..anetary studies
which antjci.pate e1.ectrj.c proculsinn systems. Wowever, c!.osed form solutions
obtainab1.e for thi.s type of system have been suggested by Goldstein et. al.,
(3.9) and Rrysnn (3.1-O) as useful. aids in studying the rendezvnlls maneuver.
The method of Bryson wi1.3. be described ri.n Section 2.3.2 and finally the
continuous low thrust studies (ti.tF linear cnst function) till be presented
in Section 2.3.3.
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