Search results for " 7"
showing 10 items of 1950 documents
Zvaigžņotā Debess: 2009, Vasara (204)
2009
Contents: E.Conners. The Trojan Asteroids ; V.Šmēlings. Men on the Moon! ; E.Bervalds. Astronomical Domes and “Sauna” ; Z.Alksne, A.Alksnis. Sakurai’s Object Fails to Escape Own Dust ; Z.Alksne, A.Alksnis. R CrB Stars Surrounded by Dust Clouds ; M.Gills. April Started with Astronomy ; A.Alksnis. First Stamps Dedicated to Astronomy by Latvia’s Post-Office ; I.Pundure. Arturs Balklavs and Astronomy of Latvia (till 1969) ; M.Sudārs. Satellite Collisions – What Threat Do They Pose? ; I.Vilks. Dwarf Planets Names in Latvian ; Announcement on the 2nd International Symposium on Dark-sky Parks: 14-19 September 2009, Slovenia ; A.Andžāns. The Best Way to Fight Darkness Is to Switch on Light (Intervi…
Zvaigžņotā Debess: 2012/13, Ziema (218)
2012
Saturs: Dienas kārtībā – «melnie caurumi» ; «Pioneer-10» dodas uz Jupiteru ; A.Alksnis. Dīvains miglājs, kam daudz nosaukumu ; M.Ņečajeva, I.Šmelds. Jonosfēras pētījumi Ventspils Starptautiskajā radioastronomijas centrā ; L.Gulbe. Satelīts ne tikai televīzijai, bet arī mežu uzraudzībai ; I.Ķešāns. Nīls Ārmstrongs ; Pirmo reizi “ZvD”: Ints Ķešāns ; E.Bervalds. Par Jāņa Ikaunieka iecerēm un VSRC (nobeigums) ; J.Dambītis, A.Cibulis. Ievērojamais Latvijas matemātiķis Arvīds Lūsis (1900–1969) ; A.Alksnis. LVU astronomijas specialitātes studenti – 1952. gada diplomandi (3.turpin.) ; I.D., I.P. Šoziem atceramies: Arturs Balklavs-Grīnhofs (2.I 1933.) – 80, Ernests Grasbergs (8.III 1938.) – 75 ; K.Š…
Optimal control of the atmospheric arc of a space shuttle and numerical simulations with multiple-shooting method
2005
This article, continuation of previous works, presents the applications of geometric optimal control theory to the analysis of the Earth re-entry problem for a space shuttle where the control is the angle of bank, the cost is the total amount of thermal flux, and the system is subject to state constraints on the thermal flux, the normal acceleration and the dynamic pressure. Our analysis is based on the evaluation of the reachable set using the maximum principle and direct computations with the boundary conditions according to the CNES research project\footnote{The project is partially supported by the Centre National d'Etude Spatiales.}. The optimal solution is approximated by a concatenat…
Geodesic flow of the averaged controlled Kepler equation
2008
A normal form of the Riemannian metric arising when averaging the coplanar controlled Kepler equation is given. This metric is parameterized by two scalar invariants which encode its main properties. The restriction of the metric to $\SS^2$ is shown to be conformal to the flat metric on an oblate ellipsoid of revolution, and the associated conjugate locus is observed to be a deformation of the standard astroid. Though not complete because of a singularity in the space of ellipses, the metric has convexity properties that are expressed in terms of the aforementioned invariants, and related to surjectivity of the exponential mapping. Optimality properties of geodesics of the averaged controll…
Second order optimality conditions in the smooth case and applications in optimal control
2007
International audience; The aim of this article is to present algorithms to compute the first conjugate time along a smooth extremal curve, where the trajectory ceases to be optimal. It is based on recent theoretical developments of geometric optimal control, and the article contains a review of second order optimality conditions. The computations are related to a test of positivity of the intrinsic second order derivative or a test of singularity of the extremal flow. We derive an algorithm called COTCOT (Conditions of Order Two and COnjugate times), available on the web, and apply it to the minimal time problem of orbit transfer, and to the attitude control problem of a rigid spacecraft. …
On local optima in minimum time control of the restricted three-body problem
2016
International audience; The structure of local minima for time minimization in the controlled three-body problem is studied. Several homotopies are systematically used to unfold the structure of these local minimizers, and the resulting singularity of the path associated with the value function is analyzed numerically.
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.
Optimal control with state constraints and the space shuttle re-entry problem
2003
In this article, we initialize the analysis under generic assumptions of the small \textit{time optimal synthesis} for single input systems with \textit{state constraints}. We use geometric methods to evaluate \textit{the small time reachable set} and necessary optimality conditions. Our work is motivated by the \textit{optimal control of the atmospheric arc for the re-entry of a space shuttle}, where the vehicle is subject to constraints on the thermal flux and on the normal acceleration. A \textit{multiple shooting technique} is finally applied to compute the optimal longitudinal arc.
On some Riemannian aspects of two and three-body controlled problems
2009
The flow of the Kepler problem (motion of two mutually attracting bodies) is known to be geodesic after the work of Moser [20], extended by Belbruno and Osipov [2, 21]: Trajectories are reparameterizations of minimum length curves for some Riemannian metric. This is not true anymore in the case of the three-body problem, and there are topological obstructions as observed by McCord et al. [19]. The controlled formulations of these two problems are considered so as to model the motion of a spacecraft within the influence of one or two planets. The averaged flow of the (energy minimum) controlled Kepler problem with two controls is shown to remain geodesic. The same holds true in the case of o…
One-parameter family of Clairaut-Liouville metrics
2007
Riemannian metrics with singularities are considered on the $2$-sphere of revolution. The analysis of such singularities is motivated by examples stemming from mechanics and related to projections of higher dimensional (regular) sub-Riemannian distributions. An unfolding of the metrics in the form of an homotopy from the canonical metric on $\SS^2$ is defined which allows to analyze the singular case as a limit of standard Riemannian ones. A bifurcation of the conjugate locus for points on the singularity is finally exhibited.