# American Institute of Mathematical Sciences

November  2005, 5(4): 929-956. doi: 10.3934/dcdsb.2005.5.929

## Geometric optimal control of elliptic Keplerian orbits

 1 Institut de Mathématiques, Université de Bourgogne, 21078 Dijon, France 2 ENSEEIHT-IRIT (UMR CNRS 5505), Institut National Polytechnique de Toulouse, 31071 Toulouse, France 3 Laboratoire d'Analyse Numérique et EDP, Université de Paris-Sud, 91405 Orsay, France

Received  November 2004 Revised  June 2005 Published  August 2005

This article deals with the transfer of a satellite between Keplerian orbits. We study the controllability properties of the system and make a preliminary analysis of the time optimal control using the maximum principle. Second order sufficient conditions are also given. Finally, the time optimal trajectory to transfer the system from an initial low orbit with large eccentricity to a terminal geostationary orbit is obtained numerically.
Citation: B. Bonnard, J.-B. Caillau, E. Trélat. Geometric optimal control of elliptic Keplerian orbits. Discrete & Continuous Dynamical Systems - B, 2005, 5 (4) : 929-956. doi: 10.3934/dcdsb.2005.5.929
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