Search results for "low thrust"

showing 3 items of 3 documents

Energy minimization of single input orbit transfer by averaging and continuation

2006

AbstractThis article deals with the transfer between Keplerian coplanar orbits using low propulsion. We focus on the energy minimization problem and compute the averaged system, proving integrability and relating the corresponding trajectories to a three-dimensional Riemannian problem that is analyzed in details. The geodesics provide approximations of the extremals of the energy minimization problem and can be used in order to evaluate the optimal trajectories of the time optimal and the minimization of the consumption problems with continuation methods. In particular, minimizing trajectories for transfer towards the geostationary orbit can be approximated in suitable coordinates by straig…

[ MATH.MATH-OC ] Mathematics [math]/Optimization and Control [math.OC]0209 industrial biotechnologyMathematics(all)GeodesicGeneral MathematicsMoyennation02 engineering and technologyPropulsionEnergy minimization01 natural sciencesContinuationAveraging020901 industrial engineering & automation0101 mathematicsMinimisation de l'énergieComputingMilieux_MISCELLANEOUSMathematicsTransfert orbital à poussée faibleMéthodes de continuation010102 general mathematicsMathematical analysis[MATH.MATH-OC] Mathematics [math]/Optimization and Control [math.OC]Orbital transfer with low thrustEnergy minimizationContinuation methodsOrbit (dynamics)Geostationary orbit[MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC]MinificationFocus (optics)
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Time Versus Energy in the Averaged Optimal Coplanar Kepler Transfer towards Circular Orbits

2015

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.

[ 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
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On the optimal control of the circular restricted three body problem

2011

The context of this work is space mechanics. More precisely, we aim at computing low thrust transfers in the Earth-Moon system modeled by the circular restricted three-body problem. The goal is to calculate the optimal steering of the spacecraft engine with respect to two optimization criteria: Final time and fuel consumption. The contributions of this thesis are of two kinds. Geometric, first, as we study the controllability of the system together with the geometry of the transfers (structure of the command) by means of geometric control tools. Numerical, then, different homotopic methods being developed. A two-three body continuation is used to compute minimum time trajectories, and then …

[ MATH.MATH-OC ] Mathematics [math]/Optimization and Control [math.OC]Earth-Moon transfercontinuations discrète et différentielletrajectoires temps ou consommation minimalesminimum time or fuel consumption trajectories[MATH.MATH-OC] Mathematics [math]/Optimization and Control [math.OC]transfert Terre-Lunecircular restricted three-body problemshootingoptimal controlcontrôle optimalpoussée faibleméthode de tirproblème des trois corps circulaire restreintlow thrust[MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC]discrete and differential continuation
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