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Habilitation à diriger des recherches

Sur la géométrie des transferts orbitaux

Abstract : The optimal control of orbital transfers is considered (problem proposed by the French Space Agency). The model is the controlled Kepler equation where the command law is the thrust of a spacecraft in orbit around the Earth. The contributions are twofold and deal with minimum time as well as with averaging of the energy minimization problem. The action of the control may be seen as the perturbation of an integrable system. Averaging then provides an approximation of this perturbation which turns to remain integrable. The exponential mapping defined by the extremal flow of the control problem is a fundamental object in this study. This mapping carries information about existence of solution, and local or global optimality of extremals. The obtained results comprise the evidence of Pi-singularities and conjugate points in minimum time, the flatness of the metric associated with energy minimum transfers towards circular orbits by averaging (optimal trajectories are straight lines), and the characterization of the cut locus of the averaged thanks to a comparison with the restriction of the flat metric to an ellipsoid of revolution.
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Habilitation à diriger des recherches
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Contributor : Jean-Baptiste Caillau <>
Submitted on : Wednesday, June 13, 2007 - 11:27:20 AM
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Jean-Baptiste Caillau. Sur la géométrie des transferts orbitaux. Mathématiques [math]. Institut National Polytechnique de Toulouse - INPT, 2006. ⟨tel-00125863v2⟩

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