Optimization of the Spacecraft Transfer Maneuver from a Point of the Elliptical Orbit to Another Point of the Same Orbit

The problem of changing the orbital position of the spacecraft located in some elliptical orbit in the Newtonian gravitational field is analyzed. It is assumed that the spacecraft is equipped with a non-adjustable engine that can be activated multiple times. An algorithm for determining the optimal (according to the criterion of the minimum characteristic velocity) transfer scheme has been developed. Special attention is paid to the analysis of the number of active segments on the trajectory and their location on the trajectory revolutions. The algorithm is based on the maximum principle and the method of parameter continuation. The initial approximation for the transfer scheme is found using the trajectory of the optimal transfer of the spacecraft with a perfectly adjustable propulsion system (engine of limited power). This trajectory is then continued for the spacecraft with a non-adjustable engine, introducing a smoothing parameter for the thrust function. In the final stage, the characteristics of the optimal transfer pattern are determined for the spacecraft with a non-adjustable engine involving a relay thrust function. The properties of the optimal scheme of the maneuver as a function of the angular distance of transfer (the number of revolutions of the trajectory) and a function of the phasing angle (the angle characterizing the angular distance between the points of the orbit where the transfer takes place) are analyzed. It is shown that an increase in the angular distance of the transfer significantly reduces the characteristic velocity of the maneuver even at large phasing angles.