Search results for " Geometry"

A predictive approach for a real-time remote visualization of large meshes

2012

Déjà sur HAL; Remote access to large meshes is the subject of studies since several years. We propose in this paper a contribution to the problem of remote mesh viewing. We work on triangular meshes. After a study of existing methods of remote viewing, we propose a visualization approach based on a client-server architecture, in which almost all operations are performed on the server. Our approach includes three main steps: a first step of partitioning the original mesh, generating several fragments of the original mesh that can be supported by the supposed smaller Transfer Control Protocol (TCP) window size of the network, a second step called pre-simplification of the mesh partitioned, ge…

La théorie des lignes parallèles de Johann Heinrich Lambert

2014

International audience; The memoir "Theory of parallel lines" (1766) by Johannes Heinrich Lambert is one of the founding texts of hyperbolic geometry, even though his author conceived it as an attempt to show that this geometry does not exist. In fact, Lambert developed that theory with the hope of finding a contradiction. In doing so, he obtained several fundamental results of hyperbolic geometry. This was sixty years before the first writings of Lobachevsky and Bolyai appeared in print. This book contains the first complete translation of Lambert's memoir as well as mathematical and historical commentaries.

Une approche géométrique du contrôle optimal de l'arc atmosphérique de la navette spatiale

2002

L'objectif de ce travail est de faire quelques remarques géométriques et des calculs préliminaires pour construire l'arc atmosphérique optimal d'une navette spatiale (problème de rentrée sur Terre ou programme d'exploration de Mars). Le système décrivant les trajectoires est de dimension 6, le contrôle est l'angle de gîte cinématique et le coût est l'intégrale du flux thermique. Par ailleurs il y a des contraintes sur l'état (flux thermique, accélération normale et pression dynamique). Notre étude est essentiellement géométrique et fondée sur une évaluation de l'ensemble des états accessibles en tenant compte des contraintes sur l'état. On esquisse une analyse des extrémales du Principe du …

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…

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.

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.

Sub-Riemannian geometry: one-parameter deformation of the Martinet flat case

1998

Topological Hopf algebras, quantum groups and deformation quantization

2003

After a presentation of the context and a brief reminder of deformation quantization, we indicate how the introduction of natural topological vector space topologies on Hopf algebras associated with Poisson Lie groups, Lie bialgebras and their doubles explains their dualities and provides a comprehensive framework. Relations with deformation quantization and applications to the deformation quantization of symmetric spaces are described

Observation of laser-induced field-free permanent planar alignment of molecules

2011

International audience; Permanent planar alignment of gas-phase linear molecules is achieved by a pair of delayed perpendicularly polarized short laser pulses. The experiment is performed in a supersonic jet, ensuring a relatively high number density of molecules with moderately low rotational temperature. The effect is optically probed on a femtosecond time scale by the use of a third short pulse, enabling a time-resolved birefringence detection performed successively in two perpendicular planes of the laboratory frame. The technique allows for an unambiguous estimation of the molecular planar delocalization produced within the polarization plane of the pulse pair after the turn-off of the…

An alternative space-time meshless method for solving transient heat transfer problems with high discontinuous moving sources

2016

International audience; The aim of this work is the development of a space-time diffuse approximation meshless method (DAM) to solve heat equations containing discontinuous sources. This work is devoted to transient heat transfer problems with static and moving heat sources applied on a metallic plate and whose power presents temporal discontinuities. The space-time DAM using classical weight function is convenient for continuous transient heat transfer. Nevertheless, for problems including discontinuities, some spurious oscillations for the temperature field occur. A new weight function, respecting the principle of causality, is used to eradicate the physically unexpected oscillations.