Time optimal slewing of a rigid body with flexible appendages

The control problem of time-optimal, rest to rest, slewing of a rigid body with flexible appendages through a large angle is considered. A finite dimesional time optimal slewing problem is proposed as a relaxation of an ill-posed infinite dimensional time optimal slewing problem. The optimal control history is shown to have an important time symmetry property. The switching times, final time and costates at mid-maneuver are shown to satisfy a system of nonlinear algebraic equations.