Illustration of the Primer Vector in Time-Fixed Orbit Transfer
In optimal (minimum-fuel) impulsive orbit transfer, few results are known
for the "time-fixed" case (prescribed transfer time) in comparison with
the known "time-open" solutions, such as the Hohmann transfer.
Time-fixed results have been reported in Refs. 3 and 4.
In this Note a technique for obtaining optimal time-fixed
impulsive solutions, applied to orbital rendezvous in Ref. 4,
is illustrated by applying it to a very simple system.
The technique is based on satisfying a set of necessary conditions (NC)
derived by Lawden and described in terms of the primer vector, the
vector of adjoint variables associated with the vehicle velocity vector.
A simple illustrative example allows an uncomplicated presentation of the
technique and yields optimal solution that are verifiable by physical
In addition it is shown that for this example the NC are also sufficient.