Quaternion Solution of the Problem of Optimal Rotation of the Orbit Plane of a Variable-Mass Spacecraft Using Thrust Orthogonal to the Orbit Plane

Abstract

The problem of the optimal rotation of the orbital plane of a spacecraft (SC) of variable mass in an inertial coordinate system is solved in a nonlinear formulation using the quaternionic differential equation of orientation of the orbital coordinate system and the Pontryagin maximum principle. The problems of speed, minimization of the thrust impulse, the spacecraft characteristic speed, and also the problems of minimizing the combined quality functionals: time and total momentum of the thrust value spent on the control process, time and the spacecraft characteristic speed are considered. Rotation of the orbital plane of the spacecraft to any angles of magnitude is controlled using the reactive thrust limited in absolute value, orthogonal to the plane of the osculating spacecraft orbit. The change in the mass of the spacecraft due to the flow of the working fluid to the control process is taken into account. A special case of the problem under study is the problem of optimal correction of the angular elements of the spacecraft orbit. The results of calculations of the optimal control of the spacecraft orbital plane by means of a small limited reactive thrust with a large number of passive and active sections of the trajectory are presented.