Investigation of the Task of the Optimal Reorientation of a Spacecraft Orbit through a Limited or Impulse Jet Thrust, Orthogonal to the Plane of the Orbit. Part 2

Abstract

This paper considers the problem of optimal reorientation of the spacecraft's orbit by a limited or pulse jet thrust which is orthogonal to the plane of the osculating orbit, with the help of quaternion differential equation of the spacecraft (SC) orbit orientation and the Pontryagin maximum principle. This kind of jet thrust changes the orientation of the spacecraft orbits while its shape and size during control process kept unchanged. Functional that defines quality of control process is a weighted convolution of two criteria: time and the total momentum of jet thrust spent on control process (special cases of this functional are fast response problem and the problem of minimizing the characteristic velocity). In the second part of the article we present a new theory of problem of optimal reorientation of the spacecraft orbit in pulse setting (using pulse (large) jet thrust). We provide algorithms for solving boundary value problems of optimal two-pulse and multi-pulse reorientation of the spacecraft orbit (non-fixed number of jet thrust pulses) and examples of numerical solution of boundary value problems of optimal reorientation of the spacecraft orbit with a limited (small) or pulse (large) thrust in which quaternion osculating element is used to describe the orientation of the spacecraft orbit.