  The minimum-fuel orbital transfer is analyzed in the case of a launcher upper
stage using a constantly thrusting engine. The thrust level is assumed to be
constant and its value is optimized together with the thrust direction. A
closed-loop solution for the thrust direction is derived from the extremal
analysis for a planar orbital transfer. The optimal control problem reduces to
two unknowns, namely the thrust level and the final time. Guessing and
propagating the costates is no longer necessary and the optimal trajectory is
easily found from a rough initialization. On the other hand the initial
costates are assessed analytically from the initial conditions and they can be
used as initial guess for transfers at different thrust levels. The method is
exemplified on a launcher upper stage targeting a geostationary transfer orbit.

Optimization and Control