The thrust minimization problem and its applications

Abstract

An indirect approach to the optimization of trajectories with finite thrust based on Pontryagin’s maximum principle is discussed. The optimization is aimed at calculating the minimum thrust for a point-to-point flight completed within a given interval of time with a constant exhaust velocity and a constant power. This may help calculate the region of existence of the optimum trajectory with thrust switching: it is evident that the latter problem may be solved if minimum thrust is lower than or equal to the available thrust in the problem with switching. A technique for calculating the optimum trajectories with a finite thrust by solving the problem of minimization of the thrust acceleration with a subsequent numerical continuation with respect to the mass flow towards the thrust minimization problem is proposed. This technique offers an opportunity to detect degeneracies associated with the lack of thrust or specific impulse. In effect, it allows one to calculate the boundaries of the region of existence of trajectories with thrust switching and thus makes it possible to automate the process of solving the problem of optimization of trajectories with thrust switching.