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Acta Applicandae Mathematicae

, Volume 135, Issue 1, pp 47–80 | Cite as

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

  • Bernard Bonnard
  • Helen C. Henninger
  • Jana Němcová
  • Jean-Baptiste PometEmail author
Article

Abstract

This article makes a study of the averaged optimal coplanar transfer towards circular orbits. Our objective is to compare this problem when the cost minimized is transfer time to the same problem when the cost minimized is energy consumption. While the minimum energy case leads to the analysis of a 2D-Riemannian metric using the standard tools of Riemannian geometry, the minimum time case is associated with 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 of the time minimal case.

Keywords

Averaging Optimal control Low thrust orbit transfer Geodesic convexity Riemann-Finsler geometry 

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Copyright information

© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  • Bernard Bonnard
    • 1
  • Helen C. Henninger
    • 2
  • Jana Němcová
    • 3
  • Jean-Baptiste Pomet
    • 2
    Email author
  1. 1.Institut de Mathématiques de BourgogneUniversité de BourgogneDijonFrance
  2. 2.Team McTAOINRIA Sophia Antipolis MéditerranéeSophia Antipolis cedexFrance
  3. 3.Department of MathematicsInstitute of Chemical TechnologyPrague 6Czech Republic

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