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

Resumo

The first part of the article provides an overview of the work on the differential equations of the spacecraft (SC) orbit orientation and the problem of optimal reorientation of a spacecraft orbit in an inertial coordinate system by means of reactive acceleration orthogonal to the osculating plane of the spacecraft. The theory of solving the problem of the optimal reorientation of the orbit of the spacecraft using the quaternionic differential equation for the orientation of the orbital coordinate system in a non-linear continuous formulation (using limited (small) thrust) is presented. As a minimized quality functional, a combined functional is used equal to the weighted sum of the reorientation time and thrust impulse (characteristic speed) during the reorientation of the orbit of the spacecraft (special cases of this functional are the speed response case and the characteristic speed minimization separately).

The theory outlined in the first part of the article is used in the second part of the article to build in a strict non-linear formulation of the new theory and new algorithms for numerical solution of the problem of the optimal reorientation of the spacecraft orbit in the inertial coordinate system by means of pulsed (high) thrust, orthogonal to the plane of an osculating orbit, using the quaternionic differential equation for the orientation of the orbital coordinate system for an unfixed number of pulses of reactive thrust. The constructed algorithms allow for the numerical solution of the problem to determine the optimal moments of switching on a reactive engine, the optimal values of reactive acceleration pulses and their optimal number. Examples are given of a numerical solution of the problem of optimal impulse reorientation of the orbit of the spacecraft, demonstrating the capabilities of the proposed method.