Optimal rotation of the orbit plane of a variable mass spacecraft in the central gravitational field by means of orthogonal thrust

With the use of quaternions and the maximum principle, we solve the optimal orbit transfer problem for a variable-mass spacecraft to a given plane in a nonlinear setting. The motion control of the spacecraft is carried out with the help of a jet thrust, bounded in absolute value and orthogonal to the plane of the osculating spacecraft orbit. We take into account the change in mass of the spacecraft due to the consumption of the working fluid in the control process. The functional that determines the quality of the control process is a linear convolution with weight factors for two criteria: time and total thrust impulse spent on the control process.
We provide an exposition of the theory of the problem’s solution. We show results of optimal control calculations for cases when both criteria are simultaneously taken into account in the minimized combined quality functional of the control process, and for cases when only the total thrust impulse is minimized. We obtain examples of optimal control with up to 192 passive and active stages. We also establish optimal control laws for the rotation of the spacecraft’s orbital plane.