Pulsed Optimal Spacecraft Orbit Reorientation by Means of Reactive Thrust Orthogonal to the Osculating Orbit. II

Abstract

A new theory and a new algorithm for numerical solution of the problem of optimal spacecraft orbit reorientation by means of a pulsed (large) thrust, orthogonal to the osculating orbit plane, for a non-fixed number of thrust impulses are set out in a strict non-linear formulation. As a control, a vector of reactive acceleration from engine thrust is used. The combined functional is minimized, equal to the weighted sum of the reorientation time and the reactive acceleration impulse (characteristic speed) during the time of the spacecraft orbit reorientation (a special case of this functional is the case of minimization of the characteristic speed). To construct the theory, a solution for the problem of optimal spacecraft orbit reorientation in continuous formulation (using limited (low) thrust) is described in the first part of this article.

It is shown that the problem of optimal impulse spacecraft orbit reorientation in the case when optimal control consists of two reactive acceleration impulses, applied to the spacecraft at initial and final moments of time of motion, is solved analytically. Examples of numerical solution of the problem of optimal impulse spacecraft orbit reorientation are given, illustrating the capabilities of the proposed method.