Search results for "orbit"
showing 10 items of 1104 documents
Conjugate and cut loci of a two-sphere of revolution with application to optimal control
2008
Abstract The objective of this article is to present a sharp result to determine when the cut locus for a class of metrics on a two-sphere of revolution is reduced to a single branch. This work is motivated by optimal control problems in space and quantum dynamics and gives global optimal results in orbital transfer and for Lindblad equations in quantum control.
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.
Minimum fuel control of the planar circular restricted three-body problem
2012
The circular restricted three-body problem is considered to model the dynamics of an artificial body submitted to the attraction of two planets. Minimization of the fuel consumption of the spacecraft during the transfer, e.g. from the Earth to the Moon, is considered. In the light of the controllability results of Caillau and Daoud (SIAM J Control Optim, 2012), existence for this optimal control problem is discussed under simplifying assumptions. Thanks to Pontryagin maximum principle, the properties of fuel minimizing controls is detailed, revealing a bang-bang structure which is typical of L1-minimization problems. Because of the resulting non-smoothness of the Hamiltonian two-point bound…
Geometric optimal control of elliptic Keplerian orbits
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.
Exploring the Solar Wind from Its Source on the Corona into the Inner Heliosphere during the First Solar Orbiter-Parker Solar Probe Quadrature
2021
This Letter addresses the first Solar Orbiter (SO) -- Parker Solar Probe (PSP) quadrature, occurring on January 18, 2021, to investigate the evolution of solar wind from the extended corona to the inner heliosphere. Assuming ballistic propagation, the same plasma volume observed remotely in corona at altitudes between 3.5 and 6.3 solar radii above the solar limb with the Metis coronagraph on SO can be tracked to PSP, orbiting at 0.1 au, thus allowing the local properties of the solar wind to be linked to the coronal source region from where it originated. Thanks to the close approach of PSP to the Sun and the simultaneous Metis observation of the solar corona, the flow-aligned magnetic fiel…
La notion de liens suffisants avec l'ordre juridique (Inlandsbeziehung) en droit international privé
2007
Optimal control and applications to orbital transfer and almost-riemannian geometry
2010
In this thesis we focus on optimal control techniques as well as geometric control techniques applied to the orbital transfer problem and to almost-Riemannian geometry. In these cases, Pontryagin’s Maximum Principle allows to analyse the extremal flow of affine control systems.In the case of a satellite with low-thrust propulsion, averaging techniques give an approximated system. Averaging is explicit in the energy minimization case and is directly related to almost-riemannian problems. The geometric analysis of such problems is generalized by the study of metrics on the two-sphere of revolution. In this way it is possible to classify the situations considering the transcendance of the solu…
Geometric optimal control : homotopic methods and applications
2012
This work is about geometric optimal control applied to celestial and quantum mechanics. We first dealt with the minimum fuel consumption problem of transfering a satellite around the Earth. This brought to the creation of the code HamPath which permits first of all to solve optimal control problem for which the command law is smooth. It is based on the Pontryagin Maximum Principle (PMP) and on the notion of conjugate point. This program combines shooting method, differential homotopic methods and tools to compute second order optimality conditions. Then we are interested in quantum control. We study first a system which consists in two different particles of spin 1/2 having two different r…
Organometallic complexes in ascidian embryonic development: II. Effects on different stages and larvae
1993
The effects of the organometallic compounds Bu2Sn-D-(−;)sorbitol, Bu2Sn-D-(+)glucose, Bu2Sn-D-(−)fructose and Bu2Sn-D-(+)glyceraldehyde were tested in vivo on different stages of Ascidian development, larval movement and metamorphosis. Organotin(IV) complexes are organometallic compounds widely used as industrial biocides, antifouling agents and agricultural fungicides and are toxic to a range of organisms. Two-cell stage embryos, if incubated for one hour in the organotin (IV) solutions, stopped the cleavage, which was restored when they were transferred into normal sea water. The gastrula stage was seriously affected in 10−4mol dm−3 solutions of the above-mentioned complexes: 85% of the e…
Design, Construction, and Characterization of a New Regioisomer and Diastereomer Material Based on the Spirooxindole Scaffold Incorporating a Sulphon…
2020
The 1,3-dipolar cycloaddition reaction is one of the most rapid, and efficient protocols to access, and construct highly divergent heterocycle chiral auxiliaries. Free catalyst synthesis of spirooxindole scaffold incorporating sulphone moiety via one pot&ndash