Comparison of the Problem of Optimizing the Trajectory of a Spacecraft with a Perfectly Adjustable Engine for Two- And Three-Channel Control in the Vicinity of a Circular Orbit

Abstract

Within the framework of this work, a comparison of the problem of optimizing the trajectory of a spacecraft with an ideally controlled engine for two- and three-channel control in the vicinity of a circular orbit is proposed. New approaches are introduced to optimize the trajectories of spacecraft in closed form for two- and three-channel control. The Hill-Clohessy-Wiltshire equations are used to describe the motion of the spacecraft in the vicinity of a circular orbit. To solve the optimal control problem, the maximum principle is used. The results of the trajectory optimization problem for two- and three-channel control are compared. Numerical examples of optimal trajectories with an ideally regulated motor in the vicinity of a circular one are given.