6533b85efe1ef96bd12bfd66

RESEARCH PRODUCT

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

Bernard BonnardJana NemcovaHelen HenningerJean-baptiste Pomet

subject

[ MATH.MATH-OC ] Mathematics [math]/Optimization and Control [math.OC]ComputationGeodesic convexity02 engineering and technologyRiemannian geometryCurvature01 natural sciencesDomain (mathematical analysis)Low thrust orbit transfersymbols.namesakeAveraging0203 mechanical engineeringFOS: MathematicsTime transferGeodesic convexityCircular orbit0101 mathematicsMathematics - Optimization and ControlMathematics020301 aerospace & aeronauticsApplied Mathematics010102 general mathematicsMathematical analysisOptimal controlOptimization and Control (math.OC)Metric (mathematics)symbolsRiemann-Finsler Geometry[MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC]Mathematics::Differential Geometry

description

International audience; 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.

yearjournalcountryeditionlanguage
2015-02-01
10.1007/s10440-014-9948-2http://arxiv.org/abs/1405.6680