The Threshold Absolute Value of a Relay Control Bringing a Satellite to a Gravitationally Stable Position in Optimal Time

Abstract

The properties of the solution to the well-known problem of the optimal orientation of a satellite in the plane of a circular orbit and its steering to a gravitationally stable angular position, which was posed and considered earlier by Vladimir V. Beletskij, have been refined. The constraint on the control torque module is considered as the main parameter of the problem. It turned out that, even in the case when the admissible control torque exceeds the gravitational moment in magnitude, in the phase plane the existence of additional switching curves corresponding to relay control with two switchings is possible. As a result, a simple numerical algorithm is proposed, and with its help the threshold absolute control value is found at which the indicated switching curves are infinitesimal, and their coordinates in the phase plane are found.