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Journal Articles Acta Applicandae Mathematicae Year : 2015

Time Versus Energy in the Averaged Optimal Coplanar Kepler Transfer towards Circular Orbits

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Abstract

The aim of this note is to compare the averaged optimal coplanar transfer towards circular orbits when the costs are the transfer time transfer and the energy consumption. While the energy case leads to analyze a 2D Riemannian metric using the standard tools of Riemannian geometry (curvature computations, geodesic convexity), the time minimal case is associated to a Finsler metric which is not smooth. Nevertheless a qualitative analysis of the geodesic flow is given in this article to describe the optimal transfers. In particular we prove geodesic convexity of the elliptic domain.
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Dates and versions

hal-00918633 , version 1 (17-12-2013)
hal-00918633 , version 2 (23-01-2014)
hal-00918633 , version 3 (26-05-2014)
hal-00918633 , version 4 (28-05-2014)
hal-00918633 , version 5 (17-06-2014)
hal-00918633 , version 6 (21-08-2015)

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Cite

Bernard Bonnard, Helen Henninger, Jana Nemcova, Jean-Baptiste Pomet. Time Versus Energy in the Averaged Optimal Coplanar Kepler Transfer towards Circular Orbits. Acta Applicandae Mathematicae, 2015, 135 (2), pp.47-80. ⟨10.1007/s10440-014-9948-2⟩. ⟨hal-00918633v6⟩
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