Optimal synthesis in the problem of uniaxial stabilization for a satellite in the case of phase constraints

The optimal stabilization problem for the pitching oscillations of a satellite is considered. For the reduced system, an optimal control problem with phase constraints is formulated and a controllability domain is constructed. A necessary optimality condition (the maximum principle for the optimal control problem with phase constraints) is used to determine optimal trajectories, the nature of interaction between a trajectory and the phase constraint boundary, and the number of boundary segments. An optimal synthesis is proposed in the constructed domain.