Averaging of Equations of Optimal Motion in Strong Central Gravitational Field with Constant and Controllable Thrust

摘要

We consider the problem of realization of orbital transfer by spacecraft with electric propulsion and maximal actual load with fixed initial mass. Traditionally this problem is subdivided into parametric and dynamic ones according to two types of engines, i.e., with constant and controllable value of thrust. We propose change of variables, which makes it possible to reduce averaged equations of optimal motion in central gravitational field with the mentioned engines to the unified form. We conduct comparison of dynamics of slow variables for some maneuvers of practical interest. It was shown that obtained by the averaging method estimate for required characteristic speed for realization of maneuver with controllable thrust does not depend on time of its realization, and value of the problem functional, i.e., integral from square of reactive acceleration, is inversely proportional to the given time of transfer.