Estimate of the control threshold value in the problem on a time-optimal satellite attitude transition maneuver

The time-optimal problem is considered for a nonlinear Lagrangian system with one degree of freedom. The system is controlled by a force bounded in absolute value, and all noncontrol forces are potential.We study the properties of optimal synthesis on the phase cylinder and indicate the conditions under which it has the simplest structure, namely, involves at most one switching for any initial conditions. The approach is used to specify the structure of the well-known solution in the classical problem on the time-optimal satellite attitude transition maneuver in the orbit plane.