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The purpose of this communication is to contribute to the development of a new trajectory management capability for an engine-out transportation aircraft. Engine-out is a dramatic situation for flight safety and this study focuses on the design of a management system for emergency trajectories at this special situation. First the gliding characteristics and flying qualities of a transport aircraft with total engine failure are analyzed while gliding range estimation is considered. Then a new representation of the flight dynamics of an engine-out aircraft is proposed where the space variable is chosen as independent parameter instead of the time variable. This allows to propose a new formulation of the corresponding trajectory optimization problem and to develop a reverse dynamic programming solution technique. Simulation results are displayed and new development perspectives are discussed.