Search results for "Orbital"
showing 10 items of 679 documents
Riemannian metric of the averaged energy minimization problem in orbital transfer with low thrust
2007
Abstract This article deals with the optimal transfer of a satellite between Keplerian orbits using low propulsion and is based on preliminary results of Epenoy et al. (1997) where the optimal trajectories of the energy minimization problem are approximated using averaging techniques. The averaged Hamiltonian system is explicitly computed. It is related to a Riemannian problem whose distance is an approximation of the value function. The extremal curves are analyzed, proving that the system remains integrable in the coplanar case. It is also checked that the metric associated with coplanar transfers towards a circular orbit is flat. Smoothness of small Riemannian spheres ensures global opti…
Optimality results in orbit transfer
2007
Abstract The objective of this Note is to present optimality results in orbital transfer. Averaging of the energy minimization problem is considered, and properties of the associated Riemannian metric are discussed. To cite this article: B. Bonnard, J.-B. Caillau, C. R. Acad. Sci. Paris, Ser. I 345 (2007).
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…
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.
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.
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…
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
X-Ray structure, Hirshfeld analysis and DFT studies of two new hits of triazolyl-indole bearing alkylsulfanyl moieties
2021
Two new hits of triazolyl-indole containing two different alkylsulfanyl analogues named tert-butyl 2-((4-amino-5-(1H-indol-2-yl)-4H-1,2,4-triazol-3-yl)thio)acetate 2, and ethyl 2-((4-amino-5-(1H-indol-2-yl)-4H-1,2,4-triazol-3-yl)thio)acetate 3 were synthesized via reaction of 4-amino-5-(1H-indol-2-yl)-1,2,4-triazol-3(2H)-thione 1 with tert-butyl bromoacetate and ethyl chloroacetate in the presence of base (Et3N). The molecular structure of 2, and 3 was confirmed by single-crystal X-ray diffraction and 1H/13C- NMR spectroscopic techniques. In compound 2, the molecular packing depends on significant O...H (9.3%), N...H (12.4%) and S...H (3.1%) as well as relatively weak C...H (14.1%), S...C (…
All-sky search in early O3 LIGO data for continuous gravitational-wave signals from unknown neutron stars in binary systems
2021
Rapidly spinning neutron stars are promising sources of continuous gravitational waves. Detecting such a signal would allow probing of the physical properties of matter under extreme conditions. A significant fraction of the known pulsar population belongs to binary systems. Searching for unknown neutron stars in binary systems requires specialized algorithms to address unknown orbital frequency modulations. We present a search for continuous gravitational waves emitted by neutron stars in binary systems in early data from the third observing run of the Advanced LIGO and Advanced Virgo detectors using the semicoherent, GPU-accelerated, binaryskyhough pipeline. The search analyzes the most s…