Controlled Transfer of a Point Mass to a Target Orbit in a Three-Dimensional Field

We consider the transfer to a given orbit of a controlled spacecraft whose dynamics is described by the mathematical model of motion in a gravitational field with one attractive center. We propose a class of engine-thrust positional controls dependent on the problem parameters that solve the controllability problem for a given target orbit. The trajectory of motion of a phase point under such control is determined on an infinite time axis. On the initial time interval, the trajectory reaches a neighborhood of the target set, and thereafter it moves in this neighborhood asymptotically approaching the target. The positional control is derived in analytical form. Calculation results are reported for the positional control and the trajectories of motion using different test parameters and different types of spacecraft target trajectories. © 2022, Springer Science+Business Media, LLC, part of Springer Nature.