Relevant bibliographies by topics / Système Lagrangien

Contents

  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers
  6. Reports

Academic literature on the topic 'Système Lagrangien'

Author: Grafiati
Published: 4 June 2021
Last updated: 2 February 2022

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Journal articles on the topic "Système Lagrangien"

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Cresson, Jacky, and Sébastien Darses. "Plongement stochastique des systèmes lagrangiens." Comptes Rendus Mathematique 342, no. 5 (March 2006): 333–36. http://dx.doi.org/10.1016/j.crma.2005.12.028.

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Wang, Qing-Guo. "Identifiability of Lagrangian Systems With Application to Robot Manipulators." Journal of Dynamic Systems, Measurement, and Control 113, no. 2 (June 1, 1991): 289–94. http://dx.doi.org/10.1115/1.2896377.

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The deterministic parameter identifiability of mechanical linear and nonlinear dynamical systems is considered via linear parameterization of system Lagrangians and necessary and sufficient conditions are established on the identifiability for linear parameters. The identifiability condition results in a new concept, the irreducible Lagrangian representation, and it is introduced to characterize a system Lagrangian with the minimal number of identifiable parameters. A linear parameterization of the Lagrangians for n-degree-of-freedom robot manipulators with rotary joints is presented and, with the help of kinematic analysis, the irreducible representations are further obtained for the PUMA 560 and planar manipulators.
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Jumarie, Guy. "A New Class of P.I.D. Parameter Adaptation Algorithms for Robot Manipulators." Robotica 9, no. 1 (January 1991): 107–9. http://dx.doi.org/10.1017/s0263574700015629.

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SUMMARYBy using very simple considerations related to the mechanical Lagrangian itself, one obtains a new general class of parameter adaptation algorithms for robot manipulators, which provides such approaches as PID adaptation schemes. These models could apply to random structural mechanical Systems, subject to the conditon that they are defined by Lagrangians.
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Billionnet, A., and S. Elloumi. "Placement de tâches dans un système distribué et dualité lagrangienne." RAIRO - Operations Research 26, no. 1 (1992): 83–97. http://dx.doi.org/10.1051/ro/1992260100831.

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CHIERCHIA, LUIGI, and FABIO PUSATERI. "Analytic Lagrangian tori for the planetary many-body problem." Ergodic Theory and Dynamical Systems 29, no. 3 (June 2009): 849–73. http://dx.doi.org/10.1017/s0143385708000503.

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AbstractIn 2004, Féjoz [Démonstration du ‘théoréme d’Arnold’ sur la stabilité du système planétaire (d’après M. Herman). Ergod. Th. & Dynam. Sys.24(5) (2004), 1521–1582], completing investigations of Herman’s [Démonstration d’un théoréme de V.I. Arnold. Séminaire de Systémes Dynamiques et manuscripts, 1998], gave a complete proof of ‘Arnold’s Theorem’ [V. I. Arnol’d. Small denominators and problems of stability of motion in classical and celestial mechanics. Uspekhi Mat. Nauk. 18(6(114)) (1963), 91–192] on the planetary many-body problem, establishing, in particular, the existence of a positive measure set of smooth (C∞) Lagrangian invariant tori for the planetary many-body problem. Here, using Rüßmann’s 2001 KAM theory [H. Rüßmann. Invariant tori in non-degenerate nearly integrable Hamiltonian systems. R. & C. Dynamics2(6) (2001), 119–203], we prove the above result in the real-analytic class.
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Fathi, Albert. "Théorème KAM faible et théorie de Mather sur les systèmes lagrangiens." Comptes Rendus de l'Académie des Sciences - Series I - Mathematics 324, no. 9 (May 1997): 1043–46. http://dx.doi.org/10.1016/s0764-4442(97)87883-4.

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Krupková, Olga. "Noether theorem and first integrals of constrained Lagrangean systems." Mathematica Bohemica 122, no. 3 (1997): 257–65. http://dx.doi.org/10.21136/mb.1997.126152.

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Mason, Evan, Francois Colas, and Josep L. Pelegrí. "A Lagrangian study tracing water parcel origins in the Canary Upwelling System." Scientia Marina 76, S1 (August 31, 2012): 79–94. http://dx.doi.org/10.3989/scimar.03608.18d.

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Gay-Balmaz, François, and Hiroaki Yoshimura. "Dirac structures and variational formulation of port-Dirac systems in nonequilibrium thermodynamics." IMA Journal of Mathematical Control and Information 37, no. 4 (July 27, 2020): 1298–347. http://dx.doi.org/10.1093/imamci/dnaa015.

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Abstract The notion of implicit port-Lagrangian systems for nonholonomic mechanics was proposed in Yoshimura & Marsden (2006a, J. Geom. Phys., 57, 133–156; 2006b, J. Geom. Phys., 57, 209–250; 2006c, Proc. of the 17th International Symposium on Mathematical Theory of Networks and Systems, Kyoto) as a Lagrangian analogue of implicit port-Hamiltonian systems. Such port-systems have an interconnection structure with ports through which power is exchanged with the exterior and which can be modeled by Dirac structures. In this paper, we present the notions of implicit port-Lagrangian systems and port-Dirac dynamical systems in nonequilibrium thermodynamics by generalizing the Dirac formulation to the case allowing irreversible processes, both for closed and open systems. Port-Dirac systems in nonequilibrium thermodynamics can be also deduced from a variational formulation of nonequilibrium thermodynamics for closed and open systems introduced in Gay-Balmaz & Yoshimura (2017a, J. Geom. Phys., 111, 169–193; 2018a, Entropy, 163, 1–26). This is a type of Lagrange–d’Alembert principle for the specific class of nonholonomic systems with nonlinear constraints of thermodynamic type, which are associated to the entropy production equation of the system. We illustrate our theory with some examples such as a cylinder-piston with ideal gas, an electric circuit with entropy production due to a resistor and an open piston with heat and matter exchange with the exterior.
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Tamminen, Eero V. "Strong Lagrange duality and the maximum principle for nonlinear discrete time optimal control problems." ESAIM: Control, Optimisation and Calculus of Variations 25 (2019): 20. http://dx.doi.org/10.1051/cocv/2018012.

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We examine discrete-time optimal control problems with general, possibly non-linear or non-smooth dynamic equations, and state-control inequality and equality constraints. A new generalized convexity condition for the dynamics and constraints is defined, and it is proved that this property, together with a constraint qualification constitute sufficient conditions for the strong Lagrange duality result and saddle-point optimality conditions for the problem. The discrete maximum principle of Pontryagin is obtained in a straightforward manner from the strong Lagrange duality theorem, first in a new form in which the Lagrangian is minimized both with respect to the state and to the control variables. Assuming differentiability, the maximum principle is obtained in the usual form. It is shown that dynamic systems satisfying a global controllability condition with convex costs, have the required convexity property. This controllability condition is a natural extension of the customary directional convexity condition applied in the derivation of the discrete maximum principle for local optima in the literature.
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Dissertations / Theses on the topic "Système Lagrangien"

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Gastou-Chassaing, Marie-Isabelle. "Chaos lagrangien entre ellipses confocales : étude théorique, numérique et expérimentale." Vandoeuvre-les-Nancy, INPL, 1995. http://www.theses.fr/1995INPL103N.

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Un fluide visqueux newtonien est introduit entre deux ellipses confocables dont les parois interne et externe peuvent être déplacées le long de leur circonférence. Une solution analytique en coordonnées elliptiques a été récemment obtenue à partir des hypothèses du régime de Stokes. Les sections de Poincaré, les points périodiques de l'écoulement et l'évolution d'une tache de traceur, montrent qu'un régime de chaos lagrangien avec de grandes surfaces potentielles de mélange peut se développer dans cette géométrie qui est également un échangeur de chaleur efficace. Le dispositif expérimental a été construit et testé. Les résultats des études théoriques et numériques ont été confrontés avec succès aux résultats expérimentaux par les méthodes suivantes: lignes de courant, déformation de taches de traceur fluorescent, sensibilité aux conditions initiales, test de nombreux profils de vitesses des parois, étude d'écoulements asymptotiques. L’analogie entre les résultats dérives de la géométrie à ellipses concentriques et de la géométrie à cercles excentrés donne des règles générales sur le comportement des mélangeurs bi-dimensionnels annulaires: importance de l'origine relative de l'énergie transférée au fluide, efficacité de l'addition de petits effets inertiels. Des applications directes importantes de cette recherche sont proposées: développement d'une méthode simple d'optimisation de mélangeurs par un choix judicieux de profils de vitesse élémentaires ; développement de nouveaux outils (sections de Poincaré et étude entropique) pour optimiser la conception de nouveaux mélangeurs
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Maftei, Radu. "Analyse stochastique pour la simulation de particules lagrangiennes : application aux collisions de particules colloïdes." Thesis, Université Côte d'Azur (ComUE), 2017. http://www.theses.fr/2017AZUR4130/document.

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Cette thèse s'inscrit dans le cadre de la simulation de particules colloïdales. Plus précisément, nous nous intéressons aux particules dans un écoulement turbulent et modélisons leur dynamique par un processus lagrangien, leurs interactions comme des collisions parfaitement élastiques où l'influence de l'écoulement est modélisée par un terme de force sur la composante vitesse du système. En couplant les particules deux par deux et considérant leurs position et vitesse relatives, la collision parfaitement élastique devient une condition de réflexion spéculaire. Nous proposons un schéma de discrétisation en temps pour le système Lagrangien résultant avec des conditions aux bords spéculaires et prouvons que l'erreur faible diminue au plus linéairement dans le pas de discrétisation temporelle. La démonstration s’appuie sur des résultats de régularité de l'EDP Feynman-Kac et requiert une certaine régularité sur le terme de force. Nous expérimentons numériquement certaines conjectures, dont l’erreur faible diminuant linéairement pour des termes de force qui ne respectent pas les conditions du théorème. Nous testons le taux de convergence de l’erreur faible pour l’extrapolation de Romberg. Enfin, nous nous intéressons aux approximations Lagrangiennes/Browniennes en considérant un système Lagrangien où la composante vitesse se comporte comme un processus rapide. Nous contrôlons l'erreur faible entre la composante position du modèle Lagrangien et un processus de diffusion uniformément elliptique. Nous démontrons ensuite un contrôle similaire en introduisant une limite réfléchissante spéculaire sur le système Lagrangien et une réflexion appropriée sur la diffusion elliptique
This thesis broadly concerns colloidal particle simulation which plays an important role in understanding two-phase flows. More specifically, we track the particles inside a turbulent flow and model their dynamics as a stochastic process, their interactions as perfectly elastic collisions where the influence of the flow is modelled by a drift on the velocity term. By coupling each particle and considering their relative position and velocity, the perfectly elastic collision becomes a specular reflection condition. We put forward a time discretisation scheme for the resulting Lagrange system with specular boundary conditions and prove that the convergence rate of the weak error decreases at most linearly in the time discretisation step. The evidence is based on regularity results of the Feynman-Kac PDE and requires some regularity on the drift. We numerically experiment a series of conjectures, amongst which the weak error linearly decreasing for drifts that do not comply with the theorem conditions. We test the weak error convergence rate for a Richardson Romberg extrapolation. We finally deal with Lagrangian/Brownian approximations by considering a Lagrangian system where the velocity component behaves as a fast process. We control the weak error between the position of the Lagrangian system and an appropriately chosen uniformly elliptic diffusion process and subsequently prove a similar control by introducing a specular reflecting boundary on the Lagrangian and an appropriate reflection on the elliptic diffusion
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Aghannan, Nasradine. "Contrôle de réacteur de polymérisation, observateur et invariance." Paris, ENMP, 2003. https://pastel.archives-ouvertes.fr/tel-00006598.

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Mehrenberger, Michel. "Inégalités d'observabilité et résolution adaptative de l'équation de Vlasov par éléments finis hiérarchiques." Université Louis Pasteur (Strasbourg) (1971-2008), 2004. http://www.theses.fr/2004STR13124.

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Frankel, Pierre. "Comportement asymptotique de systèmes dynamiques discrets et continus en Optimisation et EDP : algorithmes de minimisation proximale alternée et dynamique du deuxieme ordre à dissipation évanescente." Thesis, Montpellier 2, 2011. http://www.theses.fr/2011MON20066.

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La première partie de cette thèse (articles I et II) est consacrée à l'étude du comportement asymptotique des solutions d'un système dynamique du second ordre avec dissipation évanescente. Le système dynamique est étudié dans sa version continue et dans sa version discrète via un algorithme.La deuxième partie de cette thèse (articles III à VI) est consacrée à l'étude de plusieurs algorithmes de type proximal. Nous montrons que ces algorithmes convergent vers des solutions de certains problèmes de minimisation. Dans chaque cas, une application est donnée dans le cadre de la décomposition de domaine pour les EDP
The first part of this thesis is devoted to the study of the asymptotic behavior of solutions of a second order dynamic system with vanishing dissipation. The dynamic system is studied in its continuous version and in its discrete version via an algorithm.The second part is about the study of several proximal-type algorithms. We show that these algorithms converge to solutions of some minimization problems. In each case, an application is given in the area of domain decomposition for PDE's
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Frankel, Pierre. "Comportement asymptotique de systèmes dynamiques discrets et continus en Optimisation et EDP: algorithmes de minimisation proximale alternée et dynamique du deuxième ordre à dissipation évanescente." Phd thesis, Université Montpellier II - Sciences et Techniques du Languedoc, 2001. http://tel.archives-ouvertes.fr/tel-00637390.

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La première partie de cette thèse (articles 1 et 2) est consacrée à l'étude du comportement asymptotique des solutions de dynamiques du second ordre avec dissipation evanescente. La deuxième partie de cette thése (articles 3 à 6) est consacrée à l'étude de plusieurs algorithmes de type proximal. Nous montrons que ces algorithmes convergent vers des solutions de certains problèmes de minimisation. Dans chaque cas, une application est donnée dans le cadre de la décomposition de domaine pour les EDP.
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Baudet, Vincent. "Modélisation et simulation paramétrable d'objets déformables.Application aux traitements des cancers pulmonaires." Phd thesis, Université Claude Bernard - Lyon I, 2006. http://tel.archives-ouvertes.fr/tel-00279986.

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Les traitements curatifs des cancers par irradiation avec des rayons ionisants tels que la radiothérapie conformationnelle et l'hadronthérapie sont plannifiés avec des marges d'erreur qui prennent en compte, entre autres, les statistiques de mouvements des tumeurs.

En partenariat avec le Centre anticancéreux Léon Bérard de Lyon et dans le projet ETOILE, nous proposons de rechercher des modèles de simulations des objets déformables qui prendraient en considération, en plus de la géométrie issue directement de l'imagerie médicale, les paramètres physiologiques mesurés sur les patients afin de pouvoir garantir de meilleures marges d'erreur, dans le cas des tumeurs pulmonaires.

Dans cette thèse, nous avons choisi de modéliser les poumons avec des systèmes masses-ressorts qui sont généralement utilisés dans le monde de l'animation pour le réalisme et la rapidité.
Pour rendre le système précis et directement paramétré par les données mécaniques du patient, nous nous sommes inspirés des travaux de Van Gelder qui introduit un contrôle par les caractéristiques rhéologiques d'un matériaux "2D" linéaire élastique homogène isotrope.
Cependant, après vérification et étude théorique de ce modèle, il est apparut que celui-ci bien que donnant des animations réalistes était erroné.
Nous avons donc entrepris une étude lagrangienne qui nous a permis de rendre ce modèle 2D rectangulaire, puis 3D à base de brique élémentaire cubique, paramétrable.
Nous avons d'autre part déterminer la robustesse de notre système à l'aide de tests d'étirement, gonflement, fléchissement et cisaillement et par comparaison à des tests effectués sur des modèles éléments finis.

Cette thèse explique ainsi comment ce modèle paramétrable a été obtenu, et comment il pourra être relié avec les données physiologiques et dans quelle précision.
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Bodrero, Alain. "Contrôle d'un champ acoustique à l'intérieur d'une cavité par des moyens passifs en régime harmonique." Rouen, 1999. http://www.theses.fr/1999ROUES029.

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Le contrôle acoustique passif consiste à modifier un champ acoustique par la maîtrise des conditions aux limites. Cette technique est appliquée au cas d'une cavité munie d'une paroi vibrante en régime harmonique par optimisation des positions d'absorbeurs passifs. Une opération de sous-structuration permet de calculer la fonction de Green de la cavité aux parois réfléchissantes par la méthode des éléments finis et exprimer la pression en présence d'absorbeurs à partir de la pression en leur absence et d'un terme de correction qui tient compte de leur présence. La simulation de mesures caractéristiques du système sans absorbeur nous conduit à définir une notion de mesures numériques et remplacer les grandeurs en chaque nœud des éléments finis par leurs équivalents au centre de ces mêmes éléments. Des mesures expérimentales peuvent alors facilement être substituées à ces mesures numériques. Une méthode d'approximation assure la reconstruction du champ acoustique en présence d'absorbeurs et son gradient partout dans la cavité à partir d'un nombre fini de quantités calculées ou mesurées dans la cavité aux parois réfléchissantes. Enfin, une méthode de lagrangien augmenté rend possible la recherche de minima du niveau acoustique sous certaines contraintes géométriques. La mise en œuvre de ces techniques sur des modèles numériques a montré que l'optimisation continue des positions d'absorbeurs passifs est possible à partir d'un nombre fini de mesures et qu'il existe un nombre maximum d'absorbeurs qu'il est inutile de dépasser sous peine de nuire à l'atténuation.
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MADERNA, EZEQUIEL. "Symetries de systemes lagrangiens." Lyon, École normale supérieure (sciences), 2000. http://www.theses.fr/2000ENSL0171.

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On montre l'existence de solutions globales de viscosite pour l'equation d'hamilton-jacobi h(x, du) = c associee a un hamiltonien h convexe et superlineaire defini sur le fibre cotangent d'une variete differentiable m. Ces solutions globales sont liees a l'etude de la dynamique des courbes extremales globalement minimisantes et omega-minimisantes au sens de bangert. Parmi les systemes dynamiques consideres se trouvent les flots geodesiques des varietes riemanniennes ainsi que ceux qui proviennent de la mecanique classique entre autres. Quand le systeme presente des symetries, on montre l'existence de solutions invariantes pour des valeurs de la constante c superieures ou egales a une certaine valeur c = cinv(h). Si m est compacte, alors cinv(h) = c(h) est la valeur critique du hamiltonien, et toute solution globale est invariante par la composante neutre du groupe de symetries ; ce resultat est obtenu par l'application de la theorie de mather des mesures minimisantes, notamment du theoreme du graphe, et de la caracterisation donnee par fathi des solutions globales de viscosite. On deduit alors le corollaire suivant : toute section lagrangienne du fibre cotangent invariante par le flot hamiltonien de la fonction h est invariante par la composante neutre du groupe de symetries de h. Des exemples naturels de systemes avec groupes de symetries discrets sont donnes par les revetements. Dans ce cas, le groupe de symetries du hamiltonien releve h est le groupe d'automorphismes du revetement, et on a cinv(h) = c(h). Les revetements universel et abelien sont particulierement etudies ; si cu(h) et ca(h) sont leurs valeurs critiques respectives, et m est une variete compacte dont le groupe fondamental pi-1(m) est moyennable, on prouve que ces deux valeurs sont egales a la borne inferieure de la fonction alpha de mather.
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Chen, Y.-C. "Anti-integrability in Lagrangian systems." Thesis, University of Cambridge, 2002. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.597512.

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Three examples of application of the anti-integrability concept in Lagrangian systems are proved, concerning the continuation of a class of trajectories from the anti-integrable limit. All three examples were proposed by Robert S. MacKay. The first example arises in adiabatically perturbed systems. With an assumption that the adiabatic Poincaré-Melnikov function has simple zeros, we constructed a variational functional whose critical points give rise to a sequence of homoclinic trajectories for the unperturbed Lagrangian in the adiabatic limit but a sequence of multi-bump trajectories under perturbations. We found there is a compact set, which is a Cantor set, such that the Poincaré map induced by the phase flow restricting to it is conjugate to the Bernoulli shift, in our case, with three symbols. Hence the approach of the anti-integrability to the adiabatically perturbed problems is equivalent to the one which combines the Poincaré-Melnikov method and the Birkhoff-Smale theory. The second example occurs in the Sinai billiard system. The anti-integrable limit is the limit when the radius of the scatterer-disc goes down to zero, and the system becomes "δ-billiards". The orbits of the δ-billiards are the anti-integrable orbits which are piecewise straight lines joining zero-radius discs to discs, and are easily obtained. Under some non-degeneracy conditions, we proved all anti-integrable orbits can be continued to the small radius case, and found that any periodic orbit has infinitely many homoclinic orbits as well as heteroclinic orbits to any others. These exists a compact set, which is also a Cantor set, such that the billiard map restricted to it is conjugate to a subshift of finite type with an arbitrarily given number of symbols. We studied in the third example when the scatterers are approximated by repulsive potentials such as the Coulomb potential ε/r, where ε and r are non-negative numbers and r is the distance from the potential centre. In the Coulomb potential case, the anti-integrable limit is the ε → 0, and the system becomes the δ-billiard system. Then we found that the results in the Sinai billiards also hold here when ε > 0 but small. More general type of repulsive potentials were also investigated and a sufficient condition under which anti-integrable trajectories persist was given.
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Books on the topic "Système Lagrangien"

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Mielke, Alexander. Hamiltonian and Lagrangian flows on center manifolds: With applications to elliptic variational problems. Berlin: Springer-Verlag, 1991.

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service), SpringerLink (Online, ed. Critical Point Theory for Lagrangian Systems. Basel: Springer Basel AG, 2012.

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Ambrosetti, A. Periodic solutions of singular Lagrangian systems. Boston: Birkhäuser, 1993.

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Ambrosetti, Antonio, and Vittorio Coti Zelati. Periodic Solutions of Singular Lagrangian Systems. Boston, MA: Birkhäuser Boston, 1993. http://dx.doi.org/10.1007/978-1-4612-0319-3.

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Mazzucchelli, Marco. Critical Point Theory for Lagrangian Systems. Basel: Springer Basel, 2012. http://dx.doi.org/10.1007/978-3-0348-0163-8.

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An introduction to Lagrangian mechanics. 2nd ed. Hackensack,] New Jersey: World Scientific, 2015.

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Brizard, Alain Jean. An introduction to Lagrangian mechanics. Hackensack, NJ: World Scientific, 2008.

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Brizard, Alain Jean. An introduction to Lagrangian mechanics. Hackensack, NJ: World Scientific, 2008.

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An introduction to Lagrangian mechanics. Hackensack, NJ: World Scientific, 2008.

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Lagrangian and Hamiltonian mechanics. Singapore: World Scientific, 1996.

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Book chapters on the topic "Système Lagrangien"

1

Mielke, Alexander. "Lagrangian systems." In Hamiltonian and Lagrangian Flows on Center Manifolds, 61–83. Berlin, Heidelberg: Springer Berlin Heidelberg, 1991. http://dx.doi.org/10.1007/bfb0097550.

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Gignoux, Claude, and Bernard Silvestre-Brac. "Lagrangian Systems." In Solved Problems in Lagrangian and Hamiltonian Mechanics, 51–109. Dordrecht: Springer Netherlands, 2009. http://dx.doi.org/10.1007/978-90-481-2393-3_2.

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Després, Bruno. "Systèmes lagrangiens multidimensionnels." In Lois de Conservations Eulériennes, Lagrangiennes et Méthodes Numériques, 221–75. Berlin, Heidelberg: Springer Berlin Heidelberg, 2010. http://dx.doi.org/10.1007/978-3-642-11657-5_7.

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Prants, Sergey V., Michael Yu Uleysky, and Maxim V. Budyansky. "The Dynamical Systems Theory Approach to Transport and Mixing in Fluids." In Lagrangian Oceanography, 1–17. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-53022-2_1.

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Després, Bruno. "Systems and Lagrangian systems." In Frontiers in Mathematics, 93–163. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-50355-4_3.

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Brogliato, Bernard. "Nonsmooth Lagrangian Systems." In Communications and Control Engineering, 241–370. Cham: Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-28664-8_5.

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Ren, Wei, and Yongcan Cao. "Networked Lagrangian Systems." In Communications and Control Engineering, 147–83. London: Springer London, 2011. http://dx.doi.org/10.1007/978-0-85729-169-1_6.

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Teodorescu, Petre P. "Lagrangian Mechanics." In Mechanical Systems, Classical Models, 1–114. Dordrecht: Springer Netherlands, 2009. http://dx.doi.org/10.1007/978-90-481-2764-1_1.

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Shabana, Ahmed. "Lagrangian Dynamics." In Vibration of Discrete and Continuous Systems, 55–105. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-04348-3_2.

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Shabana, A. A. "Lagrangian Dynamics." In Vibration of Discrete and Continuous Systems, 53–97. New York, NY: Springer New York, 1997. http://dx.doi.org/10.1007/978-1-4612-4036-5_2.

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Conference papers on the topic "Système Lagrangien"

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Yoshimura, Hiroaki. "On the Lagrangian Formalism of Nonholonomic Mechanical Systems." In ASME 2005 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2005. http://dx.doi.org/10.1115/detc2005-84273.

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The paper illustrates the Lagrangian formalism of mechanical systems with nonholonomic constraints using the ideas of geometric mechanics. We first review a Lagrangian system for a conservative mechanical system in the context of variational principle of Hamilton, and we investigate the case that a given Lagrangian is hyperregular, which can be illustrated in the context of the symplectic structure on the tangent bundle of a configuration space by using the Legendre transformation. The Lagrangian system is denoted by the second order vector field and the Lagrangian one- and two-forms associated with a given hyperregular Lagrangian. Then, we demonstrate that a mechanical system with nonholonomic constraints can be formulated on the tangent bundle of a configuration manifold by using Lagrange multipliers. To do this, we investigate the Lagrange-d’Alembert principle from geometric points of view and we also show the intrinsic expression of the Lagrange-d’Alembert equations of motion for nonholonomic mechanical systems with nonconservative force fields.
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Cho, Hancheol, and Firdaus E. Udwadia. "Inverse Problem for Lagrangian Dynamics for Multi-Degree-of-Freedom Systems With Linear Damping." In ASME 2012 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2012. http://dx.doi.org/10.1115/imece2012-87196.

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This paper deals with the inverse problem for Lagrangian dynamics for linear multi-degree-of-freedom systems. New results for linearly damped systems are obtained using extensions of results for single-degree-of-freedom systems. First, for a two-degree-of-freedom linear system with linear damping, the conditions for the existence of a Lagrangian are explicitly obtained by solving the Helmholtz conditions. Next, since the Helmholtz conditions are near-impossible to solve for general n-degree-of-freedom systems, a new simple procedure that does not require the use of the Helmholtz conditions and that is easily extended to n-degree-of-freedom linear systems, is developed. The emphasis is on obtaining the Lagrangians for these multi-degree-of-freedom systems in a simple manner, using insights obtained from our understanding of the inverse problem for single- and two-degree-of-freedom systems. Specifically we include systems that commonly arise in linear vibration theory with positive definite mass matrices, and symmetric stiffness and damping matrices. This method yields several new Lagrangians for linear multi-degree-of-freedom systems. Finally, conservation laws for these damped multi-degree-of-freedom systems are found using the Lagrangians obtained.
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Yoshimura, Hiroaki. "A Geometric Approach to Constraint Stabilization for Holonomic Lagrangian Systems." In ASME 2007 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2007. http://dx.doi.org/10.1115/detc2007-35429.

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In this paper, we develop a geometric approach to constraint stabilization for holonomic mechanical systems in the context of Lagrangian formulation. We first show that holonomic mechanical systems, for the case in which a given Lagrangian is hyperregular, can be formulated by using the Lagrangian two-form, namely, a symplectic structure on the tangent bundle of a configuration manifold that is induced from the cotangent bundle via the Legendre transformation. Then, we present an idea of geometric constraint stabilization and we show that a holonomic Lagrangian system with geometric constraint stabilization can be formulated by the Lagrange-d’Alembert principle, together with its local coordinate expression for the sake of numerical computations. Finally, we illustrate the numerical verification that the proposed method enables to stabilize constraint violations effectively in comparison with the Baumgarte and Gear–Gupta–Leimkuhler methods together with an example of a linkage mechanism.
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Gou Nishida, Masaki Yamakita, and Zhi-wei Luo. "Field port-Lagrangian systems with degenerate Lagrangian and external forces." In 2007 46th IEEE Conference on Decision and Control. IEEE, 2007. http://dx.doi.org/10.1109/cdc.2007.4434261.

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Baleanu, Dumitru, and Sami I. Muslih. "About Lagrangian Formulation of Classical Fields Within Riemann-Liouville Fractional Derivatives." In ASME 2005 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2005. http://dx.doi.org/10.1115/detc2005-84390.

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Recently, an extension of the simplest fractional problem and the fractional variational problem of Lagrange was obtained by Agrawal. The first part of this study presents the fractional Lagrangian formulation of mechanical systems and introduce the Levy path integral. The second part is an extension to Agrawal’s approach to classical fields with fractional derivatives. The classical fields with fractional derivatives are investigated by using the Lagrangian formulation. The case of the fractional Schro¨dinger equation is presented.
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"Lagrangian Road Pricing." In International Conference on Operations Research and Enterprise Systems. SciTePress - Science and and Technology Publications, 2013. http://dx.doi.org/10.5220/0004287102920297.

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Feeny, B. F. "D’Alembert’s Principle and the Equations of Motion for Nonholonomic Systems." In ASME 2006 International Mechanical Engineering Congress and Exposition. ASMEDC, 2006. http://dx.doi.org/10.1115/imece2006-14533.

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D'Alembert's principle is manipulated in the presence of nonholonomic constraints to derive the principle of virtual power in nonholonomic form, and Lagrange's equations for nonholonomic systems. The Lagrangian equations had been expressed previously for conservative systems, derived by variational methods. The D'Alembert derivation confirms the roles of constrained and unconstrained Lagrangians directly by the presence of constrained and unconstrained velocities in D'Alembert's principle. The constrained form of nonconservative generalized forces is also determined for both particles and rigid bodies. An example is a rolling disk.
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Nacivet, Samuel, Christophe Pierre, Fabrice Thouverez, and Louis Jezequel. "Analysis of Periodic Frictional Contact in Finite Elements Problems." In ASME 2001 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2001. http://dx.doi.org/10.1115/detc2001/vib-21735.

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Abstract This paper considers the dynamics of structural systems modeled using the finite element method and subject to dry friction damping, using Coulomb’s law for the friction force model. A new frequency-time domain method, the Dynamic Lagrangian mixed Frequency-Time method (DLFT), is developed to calculate the steady-state forced response. The dynamic Lagrangians formulation introduced herein, when used in conjunction with a nonlinear solver in the frequency domain, is better suited to handling dry friction nonlinearities than the traditional augmented Lagrangians method. Namely, the use of dynamic Lagrangians allows one to solve for the nonlinear forces between two finite element nodes of the structure without using artifacts such as a spring. Hence the finite element model does not have to be degraded at the contact interface. Furthermore, a new reduction of the nonlinear system is proposed to decrease the required computation time. Finally, a set of numerical examples is presented for a beam in contact with a flexible dry friction element connected to ground, for frictional constraints that feature two-dimensional relative motion, and for a large-scale structural system with many friction dampers.
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Frye, Jason P., and Brian C. Fabien. "Control of Constrained Systems Described by Lagrangian DAEs." In ASME 2011 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2011. http://dx.doi.org/10.1115/detc2011-47502.

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In this paper, a nonlinear controller design for constrained systems described by Lagrangian differential algebraic equations (DAEs) is presented. The controller design utilizes the structure introduced by the coordinate splitting formulation, a numerical technique used for integration of DAEs. In this structure, the Lagrange multipliers associated with the constraint equations are eliminated, and the equations of motion are transformed into implicit differential equations. Making use of this, a feedback linearizing controller can be chosen for successful motion tracking of the constrained system. Numerical examples demonstrate the controller design can be successfully applied to fully actuated and underactuated systems.
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Koganezawa, Koichi, and Kazuomi Kaneko. "ODE Methods for Solving the Multibody Dynamics With Constraints." In ASME 1999 Design Engineering Technical Conferences. American Society of Mechanical Engineers, 1999. http://dx.doi.org/10.1115/detc99/vib-8237.

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Abstract This paper deals with methods for solving the multi-body dynamics with constraints. The problem is considered in the framework of solving the Lagrange multipliers in addition to the system coordinates in the differential and algebraic equation (DAE) governing the dynamics with holonomic or non-holonoinic constraints. The proposed methods are originally based on Baumgarte’s work for the holonomic constraints but its extensions. First, one considers a Lagrangian which includes the time-differentiated constraint equations in addition to the constraint equations themselves. Applying the Lagrange procedure we have the ordinary differential equations (ODE), not the DAE, including the differential equation with respect to the Lagrange multipliers. This paper also presents a numerically stable method for inverting the system matrix. The numerical solution for the differential equations with respect to the Lagrange multipliers as well as the system coordinates by using the ordinary numerical integration method, e.g. Runge-Kutta method, shows the excellent stability of the constraints, which is superior to the penalty method.
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Reports on the topic "Système Lagrangien"

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Thierauf, Rainer. A Lagrangian for a system of two dyons. Portland State University Library, January 2000. http://dx.doi.org/10.15760/etd.5712.

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Felmer, Patricio L. Multiple Solutions for Lagrangian Systems in T Superscript n. Fort Belvoir, VA: Defense Technical Information Center, July 1989. http://dx.doi.org/10.21236/ada210646.

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Bernatska, Julia, and Petro Holod. • Harmonic Analysis on Lagrangian Manifolds of Integrable Hamiltonian Systems. GIQ, 2012. http://dx.doi.org/10.7546/giq-14-2013-61-73.

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Bernatska and Petro Holod, Julia Bernatska and Petro Holod. Harmonic Analysis on Lagrangian Manifolds of Integrable Hamiltonian Systems. Journal of Geometry and Symmetry in Physics, 2013. http://dx.doi.org/10.7546/jgsp-29-2013-39-51.

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Ide, Kayo. An Operational Technology for Assimilating Lagrangian Data Based on Dynamical Systems Techniques. Fort Belvoir, VA: Defense Technical Information Center, September 2006. http://dx.doi.org/10.21236/ada613573.

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Ide, Kayo. An Operational Technology for Assimilating Lagrangian Data Based on Dynamical Systems Techniques. Fort Belvoir, VA: Defense Technical Information Center, September 2008. http://dx.doi.org/10.21236/ada534008.

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Jones, Christopher K. An Operational Technology for Assimilating Lagrangian Data Based on Dynamical Systems Techniques. Fort Belvoir, VA: Defense Technical Information Center, September 2008. http://dx.doi.org/10.21236/ada534142.

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Ide, Kayo. An Operational Technology for Assimilating Lagrangian Data Based on Dynamical Systems Techniques. Fort Belvoir, VA: Defense Technical Information Center, September 2007. http://dx.doi.org/10.21236/ada573119.

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Jones, Christopher K. An Operational Technology for Assimilating Lagrangian Data Based on Dynamical Systems Techniques. Fort Belvoir, VA: Defense Technical Information Center, September 2007. http://dx.doi.org/10.21236/ada573394.

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Jones, Christopher K. An Operational Technology for Assimilating Lagrangian Data Based on Dynamical Systems Techniques. Fort Belvoir, VA: Defense Technical Information Center, September 2006. http://dx.doi.org/10.21236/ada630941.

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