SINGULAR ARCS FOR BLUNT ENDOATMOSPHERIC VEHICLES

This paper formulates the Mayer optimal control problem for an endoatm ospheric, non-lifting, finite-thrust vehicle, and considers singular e xtremals. Using Lie brackets, the singular control is derived and expr essed in a state feedback form. The totality of extremals indicates th at a forced Keplerian motion obtained by thrust-drag cancellation is n ot optimal for any Mayer performance criterion. In addition, this pape r proves two theorems establishing limits on the optimality of bang-ba ng control for such a system, and develops a heuristic for the suffici ency of bang-bang optimal control. A sample problem of optimal orbital maintenance indicates the importance of thrust-vectoring for greater propellant efficiency.