Relevant bibliographies by topics / Hamiltonian and Lagrangian dynamics

Contents

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

Academic literature on the topic 'Hamiltonian and Lagrangian dynamics'

Author: Grafiati
Published: 4 June 2021
Last updated: 1 February 2022

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Journal articles on the topic "Hamiltonian and Lagrangian dynamics"

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Cheng, Xu-Hui, and Guo-Qing Huang. "A Comparison between Second-Order Post-Newtonian Hamiltonian and Coherent Post-Newtonian Lagrangian in Spinning Compact Binaries." Symmetry 13, no. 4 (April 1, 2021): 584. http://dx.doi.org/10.3390/sym13040584.

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In relativistic celestial mechanics, post-Newtonian (PN) Lagrangian and PN Hamiltonian formulations are not equivalent to the same PN order as our previous work in PRD (2015). Usually, an approximate Lagrangian is used to discuss the difference between a PN Hamiltonian and a PN Lagrangian. In this paper, we investigate the dynamics of compact binary systems for Hamiltonians and Lagrangians, including Newtonian, post-Newtonian (1PN and 2PN), and spin–orbit coupling and spin–spin coupling parts. Additionally, coherent equations of motion for 2PN Lagrangian are adopted here to make the comparison with Hamiltonian approaches and approximate Lagrangian approaches at the same condition and same PN order. The completely opposite nature of the dynamics shows that using an approximate PN Lagrangian is not convincing. Hence, using the coherent PN Lagrangian is necessary for obtaining an exact result in the research of dynamics of compact binary at certain PN order. Meanwhile, numerical investigations from the spinning compact binaries show that the 2PN term plays an important role in causing chaos in the PN Hamiltonian system.
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Rosas-Ortiz, Oscar. "Lagrangian and Hamiltonian dynamics." Contemporary Physics 60, no. 1 (January 2, 2019): 85–86. http://dx.doi.org/10.1080/00107514.2019.1580314.

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MALIK, R. P. "HAMILTONIAN AND LAGRANGIAN DYNAMICS IN A NONCOMMUTATIVE SPACE." Modern Physics Letters A 18, no. 39 (December 21, 2003): 2795–806. http://dx.doi.org/10.1142/s0217732303012350.

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We discuss the dynamics of a particular two-dimensional (2D) physical system in the four-dimensional (4D) (non-)commutative phase space by exploiting the consistent Hamiltonian and Lagrangian formalisms based on the symplectic structures defined on the 4D (non-)commutative cotangent manifolds. The noncommutativity exists equivalently in the coordinate or the momentum planes embedded in the 4D cotangent manifolds. The signature of this noncommutativity is reflected in the derivation of the first-order Lagrangians where we exploit the most general form of the Legendre transformation defined on the (non-)commutative (co-)tangent manifolds. The second-order Lagrangian, defined on the 4D tangent manifold, turns out to be the same irrespective of the noncommutativity present in the 4D cotangent manifolds for the discussion of the Hamiltonian formulation. A connection with the noncommutativity of the dynamics, associated with the quantum groups on the q-deformed 4D cotangent manifolds, is also pointed out.
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Wheeler, James T. "Not-so-classical mechanics: unexpected symmetries of classical motion." Canadian Journal of Physics 83, no. 2 (February 1, 2005): 91–138. http://dx.doi.org/10.1139/p05-003.

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A survey of topics of recent interest in Hamiltonian and Lagrangian dynamical systems, including accessible discussions of regularization of the central-force problem; inequivalent Lagrangians and Hamiltonians; constants of central-force motion; a general discussion of higher order Lagrangians and Hamiltonians, with examples from Bohmian quantum mechanics, the Korteweg–de Vries equation, and the logistic equation; gauge theories of Newtonian mechanics; and classical spin, Grassmann numbers, and pseudomechanics. PACS No.: 45.25.Jj
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KIJOWSKI, J., G. MAGLI, and D. MALAFARINA. "LAGRANGIAN AND HAMILTONIAN FORMULATION OF SPHERICAL SHELL DYNAMICS." International Journal of Geometric Methods in Modern Physics 02, no. 05 (October 2005): 887–94. http://dx.doi.org/10.1142/s021988780500082x.

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Lagrangian and Hamiltonian descriptions of the dynamics of a self-gravitating matter shell in General Relativity are discussed in general. The case of a spherical shell composed of an elastic fluid is then considered, its Lagrangian function is derived from first principles and the Hamiltonian is calculated. Known results for dust shells are recovered as particular cases.
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Entov, Michael, and Leonid Polterovich. "Lagrangian tetragons and instabilities in Hamiltonian dynamics." Nonlinearity 30, no. 1 (November 17, 2016): 13–34. http://dx.doi.org/10.1088/0951-7715/30/1/13.

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Bernard, Patrick. "The Lax–Oleinik semi-group: a Hamiltonian point of view." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 142, no. 6 (November 27, 2012): 1131–77. http://dx.doi.org/10.1017/s0308210511000059.

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The weak KAM theory was developed by Fathi in order to study the dynamics of convex Hamiltonian systems. It somehow makes a bridge between viscosity solutions of the Hamilton–Jacobi equation and Mather invariant sets of Hamiltonian systems, although this was fully understood only a posteriori. These theories converge under the hypothesis of convexity, and the richness of applications mostly comes from this remarkable convergence. In this paper, we provide an elementary exposition of some of the basic concepts of weak KAM theory. In a companion paper, Albert Fathi exposed the aspects of his theory which are more directly related to viscosity solutions. Here, on the contrary, we focus on dynamical applications, even if we also discuss some viscosity aspects to underline the connections with Fathi's lecture. The fundamental reference on weak KAM theory is the still unpublished book Weak KAM theorem in Lagrangian dynamics by Albert Fathi. Although we do not offer new results, our exposition is original in several aspects. We only work with the Hamiltonian and do not rely on the Lagrangian, even if some proofs are directly inspired by the classical Lagrangian proofs. This approach is made easier by the choice of a somewhat specific setting. We work on ℝd and make uniform hypotheses on the Hamiltonian. This allows us to replace some compactness arguments by explicit estimates. For the most interesting dynamical applications, however, the compactness of the configuration space remains a useful hypothesis and we retrieve it by considering periodic (in space) Hamiltonians. Our exposition is centred on the Cauchy problem for the Hamilton–Jacobi equation and the Lax–Oleinik evolution operators associated to it. Dynamical applications are reached by considering fixed points of these evolution operators, the weak KAM solutions. The evolution operators can also be used for their regularizing properties; this opens an alternative route to dynamical applications.
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Bokhove, Onno, and Marcel Oliver. "Parcel Eulerian–Lagrangian fluid dynamics of rotating geophysical flows." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 462, no. 2073 (March 30, 2006): 2575–92. http://dx.doi.org/10.1098/rspa.2006.1656.

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Parcel Eulerian–Lagrangian Hamiltonian formulations have recently been used in structure-preserving numerical schemes, asymptotic calculations and in alternative explanations of fluid parcel (in)stabilities. A parcel formulation describes the dynamics of one fluid parcel with a Lagrangian kinetic energy but an Eulerian potential evaluated at the parcel's position. In this paper, we derive the geometric link between the parcel Eulerian–Lagrangian formulation and well-known variational and Hamiltonian formulations for three models of ideal and geophysical fluid flow: generalized two-dimensional vorticity–stream function dynamics, the rotating two-dimensional shallow-water equations and the rotating three-dimensional compressible Euler equations.
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Zivieri, Roberto, and Giancarlo Consolo. "Hamiltonian and Lagrangian Dynamical Matrix Approaches Applied to Magnetic Nanostructures." Advances in Condensed Matter Physics 2012 (2012): 1–16. http://dx.doi.org/10.1155/2012/765709.

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Two micromagnetic tools to study the spin dynamics are reviewed. Both approaches are based upon the so-called dynamical matrix method, a hybrid micromagnetic framework used to investigate the spin-wave normal modes of confined magnetic systems. The approach which was formulated first is the Hamiltonian-based dynamical matrix method. This method, used to investigate dynamic magnetic properties of conservative systems, was originally developed for studying spin excitations in isolated magnetic nanoparticles and it has been recently generalized to study the dynamics of periodic magnetic nanoparticles. The other one, the Lagrangian-based dynamical matrix method, was formulated as an extension of the previous one in order to include also dissipative effects. Such dissipative phenomena are associated not only to intrinsic but also to extrinsic damping caused by injection of a spin current in the form of spin-transfer torque. This method is very accurate in identifying spin modes that become unstable under the action of a spin current. The analytical development of the system of the linearized equations of motion leads to a complex generalized Hermitian eigenvalue problem in the Hamiltonian dynamical matrix method and to a non-Hermitian one in the Lagrangian approach. In both cases, such systems have to be solved numerically.
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MUKHANOV, V., and A. WIPF. "ON THE SYMMETRIES OF HAMILTONIAN SYSTEMS." International Journal of Modern Physics A 10, no. 04 (February 10, 1995): 579–610. http://dx.doi.org/10.1142/s0217751x95000267.

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In this paper we show how the well-known local symmetries of Lagrangian systems, and in particular the diffeomorphism invariance, emerge in the Hamiltonian formulation. We show that only the constraints which are linear in the momenta generate transformations which correspond to symmetries of the corresponding Lagrangian system. The non-linear constraints (which we have, for instance, in gravity, supergravity and string theory) generate the dynamics of the corresponding Lagrangian system. Only in a very special combination with "trivial" transformations proportional to the equations of motion do they lead to symmetry transformations. We show the importance of these special "trivial" transformations for the interconnection theorems which relate the symmetries of a system with its dynamics. We prove these theorems for general Hamiltonian systems. We apply the developed formalism to concrete physically relevant systems, in particular those which are diffeomorphism-invariant. The connection between the parameters of the symmetry transformations in the Hamiltonian and Lagrangian formalisms is found. The possible applications of our results are discussed.
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Dissertations / Theses on the topic "Hamiltonian and Lagrangian dynamics"

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Foxman, Jerome Adam. "The Maslov index in Hamiltonian dynamical systems." Thesis, University of Bristol, 2000. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.326680.

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Hosein, Falahaty. "Enhanced fully-Lagrangian particle methods for non-linear interaction between incompressible fluid and structure." Kyoto University, 2018. http://hdl.handle.net/2433/235070.

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Rypina, Irina I. "Lagrangian Coherent Structures and Transport in Two-Dimensional Incompressible Flows with Oceanographic and Atmospheric Applications." Scholarly Repository, 2007. http://scholarlyrepository.miami.edu/oa_dissertations/14.

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The Lagrangian dynamics of two-dimensional incompressible fluid flows is considered, with emphasis on transport processes in atmospheric and oceanic flows. The dynamical-systems-based approach is adopted; the Lagrangian motion in such systems is studied with the aid of Kolmogorov-Arnold-Moser (KAM) theory, and results relating to stable and unstable manifolds and lobe dynamics. Some nontrivial extensions of well-known results are discussed, and some extensions of the theory are developed. In problems for which the flow field consists of a steady background on which a time-dependent perturbation is superimposed, it is shown that transport barriers arise naturally and play a critical role in transport processes. Theoretical results are applied to the study of transport in measured and simulated oceanographic and atmospheric flows. Two particular problems are considered. First, we study the Lagrangian dynamics of the zonal jet at the perimeter of the Antarctic Stratospheric Polar Vortex during late winter/early spring within which lies the "ozone hole". In this system, a robust transport barrier is found near the core of a zonal jet under typical conditions, which is responsible for trapping of the ozone-depleted air within the ozone hole. The existence of such a barrier is predicted theoretically and tested numerically with use of a dynamically-motivated analytically-prescribed model. The second, oceanographic, application considered is the study of the surface transport in the Adriatic Sea. The surface flow in the Adriatic is characterized by a robust threegyre background circulation pattern. Motivated by this observation, the Lagrangian dynamics of a perturbed three-gyre system is studied, with emphasis on intergyre transport and the role of transport barriers. It is shown that a qualitative change in transport properties, accompanied by a qualitative change in the structure of stable and unstable manifolds occurs in the perturbed three-gyre system when the perturbation strength exceeds a certain threshold. This behavior is predicted theoretically, simulated numerically with use of an analytically prescribed model, and shown to be consistent with a fully observationally-based model.
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Mehrmann, Volker, and Hongguo Xu. "Lagrangian invariant subspaces of Hamiltonian matrices." Universitätsbibliothek Chemnitz, 2005. http://nbn-resolving.de/urn:nbn:de:swb:ch1-200501133.

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The existence and uniqueness of Lagrangian invariant subspaces of Hamiltonian matrices is studied. Necessary and sufficient conditions are given in terms of the Jordan structure and certain sign characteristics that give uniqueness of these subspaces even in the presence of purely imaginary eigenvalues. These results are applied to obtain in special cases existence and uniqueness results for Hermitian solutions of continuous time algebraic Riccati equations.
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Schwingenheuer, Martin. "Hamiltonian unknottedness of certain monotone Lagrangian tori in S2xS2." Diss., lmu, 2010. http://nbn-resolving.de/urn:nbn:de:bvb:19-123969.

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Faber, Nicolas Boily Christian M. Portegies Zwart Simon. "Orbital complexity in Hamiltonian dynamics." Strasbourg : Université de Starsbourg, 2009. http://eprints-scd-ulp.u-strasbg.fr:8080/secure/00001111/01/FABER_Nicolas_2008-restrict.pdf.

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Thèse de doctorat : Astrophysique : Strasbourg 1 : 2008. Thèse de doctorat : Astrophysics : Universiteit van Amsterdam, Nederland : 2008.
Thèse soutenue sur un ensemble de travaux. Thèse soutenue en co-tutelle. Titre provenant de l'écran-titre. Notes bibliogr.
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Faber, Nicolas. "Orbital complexity in Hamiltonian dynamics." Université Louis Pasteur (Strasbourg) (1971-2008), 2008. https://publication-theses.unistra.fr/restreint/theses_doctorat/2008/FABER_Nicolas_2008.pdf.

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L’observation d’un phénomène physique s’appuie en général sur l’évolution d’une observable en fonction du temps. Une telle série temporelle contient les informations de base sur l’état du système étudié. Dans cette thèse, nous exploitons ce concept afin d’explorer l’évolution dynamique complexe qui peut avoir lieu dans les systèmes autogravitants Hamiltoniens. Nous traitons les coordonnées dans l’espace des phases des corps célestes comme des signaux, que nous analysons par la suite en utilisant différentes méthodes de traitement du signal, plus particulièrement la fonction d’autocorrélation et la transformée d’ondelettes. Dans notre analyse nous considérons tour à tour la dynamique à grande échelle des galaxies et celle, interne, des amas stellaires denses
The monitoring of physical phenomena (often) rests on a mapping of an observable as a function of time. Such time series encode basic information about the state of the system under study. In this thesis, we build on this concept to explore the intricate evolution of gravitational Hamiltonian systems. We treat the phase-space coordinates of celestial bodies as signals which we then analyze using processing techniques, such as autocorrelation identification and wavelet transforms. We consider in turn the large-scale dynamics of galaxies, and the internal dynamics of dense stellar clusters. [. . . ]
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Schöberl, Markus. "Geometry and control of mechanical systems an Eulerian, Lagrangian and Hamiltonian approach." Aachen Shaker, 2007. http://d-nb.info/989019306/04.

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Salmon, Daniel. "Dynamics of Systems With Hamiltonian Monodromy." W&M ScholarWorks, 2018. https://scholarworks.wm.edu/etd/1550153890.

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A system is said to have monodromy if, when we carry the system around a closed circuit, it does not return to its initial state. The simplest example is the square-root function in the complex plane. A Hamiltonian system is said to have Hamiltonian monodromy if its fundamental action-angle loops do not return to their initial topological state at the end of a closed circuit. These changes in topology of angle loops carry through to other aspects of these systems, including the classical dynamics of families of trajectories, quantum spectra and even wavefunctions. This topological change in the evolution of a loop of classical trajectories has been observed experimentally for the rst time, using an apparatus consisting of a spherical pendulum subject to magnetic potentials and torques. Presented in this dissertation are the details of this experiment, as well as theoretical calculations on a novel system: a double welled Mexican-hat system with two monodromy points. This is part of a more general research program that is concerned with the Lagrangian torus bration of the phase spaces of integrable Hamiltonian systems. It is in this way the calculations on the double welled system are carried out. in this dissertation, static and dynamical manifestations of monodromy are shown to exist for this system. It has been shown previously that corresponding topological changes occur in wavefunctions of systems with monodromy. Here it is shown that results of quantum wavefunction monodomy carry over intuitively.
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Prieto, Martínez Pere Daniel. "Geometrical structures of higher-order dynamical systems and field theories." Doctoral thesis, Universitat Politècnica de Catalunya, 2014. http://hdl.handle.net/10803/284215.

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Geometrical physics is a relatively young branch of applied mathematics that was initiated by the 60's and the 70's when A. Lichnerowicz, W.M. Tulczyjew and J.M. Souriau, among many others, began to study various topics in physics using methods of differential geometry. This "geometrization" provides a way to analyze the features of the physical systems from a global viewpoint, thus obtaining qualitative properties that help us in the integration of the equations that describe them. Since then, there has been a strong development in the intrinsic treatment of a variety of topics in theoretical physics, applied mathematics and control theory using methods of differential geometry. Most of the work done in geometrical physics since its first days has been devoted to study first-order theories, that is, those theories whose physical information depends on (at most) first-order derivatives of the generalized coordinates of position (velocities). However, there are theories in physics in which the physical information depends explicitly on accelerations or higher-order derivatives of the generalized coordinates of position, and thus more sophisticated geometrical tools are needed to model them acurately. In this Ph.D. Thesis we pretend to give a geometrical description of some of these higher-order theories. In particular, we focus on dynamical systems and field theories whose dynamical information can be given in terms of a Lagrangian function, or a Hamiltonian that admits Lagrangian counterpart. More precisely, we will use the Lagrangian-Hamiltonian unified approach in order to develop a geometric framework for autonomous and non-autonomous higher-order dynamical system, and for second-order field theories. This geometric framework will be used to study several relevant physical examples and applications, such as the Hamilton-Jacobi theory for higher-order mechanical systems, relativistic spin particles and deformation problems in mechanics, and the Korteweg-de Vries equation and other systems in field theory.
La física geomètrica és una branca relativament jove de la matemàtica aplicada que es va iniciar als anys 60 i 70 qua A. Lichnerowicz, W.M. Tulczyjew and J.M. Souriau, entre molts altres, van començar a estudiar diversos problemes en física usant mètodes de geometria diferencial. Aquesta "geometrització" proporciona una manera d'analitzar les característiques dels sistemes físics des d'una perspectiva global, obtenint així propietats qualitatives que faciliten la integració de les equacions que els descriuen. D'ençà s'ha produït un fort desenvolupamewnt en el tractament intrínsic d'una gran varietat de problemes en física teòrica, matemàtica aplicada i teoria de control usant mètodes de geometria diferencial. Gran part del treball realitzat en la física geomètrica des dels seus primers dies s'ha dedicat a l'estudi de teories de primer ordre, és a dir, teories tals que la informació física depèn en, com a molt, derivades de primer ordre de les coordenades de posició generalitzades (velocitats). Tanmateix, hi ha teories en física en les que la informació física depèn de manera explícita en acceleracions o derivades d'ordre superior de les coordenades de posició generalitzades, requerint, per tant, d'eines geomètriques més sofisticades per a modelar-les de manera acurada. En aquesta Tesi Doctoral ens proposem donar una descripció geomètrica d'algunes d'aquestes teories. En particular, estudiarem sistemes dinàmics i teories de camps tals que la seva informació dinàmica ve donada en termes d'una funció lagrangiana, o d'un hamiltonià que prové d'un sitema lagrangià. Per a ser més precisos emprarem la formulació unificada Lagrangiana-Hamiltoniana per tal de desenvolupar marcs geomètrics per a sistemes dinàmics d'ordre superior autònoms i no autònoms, i per a teories de camps de segon ordre. Amb aquest marc geomètric estudiarem alguns exemples físics rellevants i algunes aplicacions, com la teoria de Hamilton-Jacobi per a sistemes mecànics d'ordre superior, partícules relativístiques amb spin i problemes de deformació en mecànica, i l'equació de Korteweg-de Vries i altres sistemes en teories de camps.
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Books on the topic "Hamiltonian and Lagrangian dynamics"

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Lee, Taeyoung, Melvin Leok, and N. Harris McClamroch. Global Formulations of Lagrangian and Hamiltonian Dynamics on Manifolds. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-56953-6.

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Baldomá, Inmaculada. Exponentially small splitting of invariant manifolds of parabolic points. Providence, RI: American Mathematical Society, 2004.

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

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Hamiltonian dynamics. River Edge, NJ: World Scientific, 2001.

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Deriglazov, Alexei. Classical mechanics: Hamiltonian and Lagrangian Formalism. Berlin: Springer Verlag, 2010.

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Classical mechanics: Hamiltonian and Lagrangian Formalism. Berlin: Springer Verlag, 2010.

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Bennett, Andrew F. Lagrangian fluid dynamics. Cambridge: Cambridge University Press, 2005.

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Bountis, Tassos, and Haris Skokos. Complex Hamiltonian Dynamics. Berlin, Heidelberg: Springer Berlin Heidelberg, 2012. http://dx.doi.org/10.1007/978-3-642-27305-6.

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Haris, Skokos, ed. Complex Hamiltonian dynamics. Heidelberg: Springer, 2012.

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

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Book chapters on the topic "Hamiltonian and Lagrangian dynamics"

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Enns, Richard H., and George C. McGuire. "Lagrangian & Hamiltonian Dynamics." In Computer Algebra Recipes for Classical Mechanics, 211–54. Boston, MA: Birkhäuser Boston, 2003. http://dx.doi.org/10.1007/978-1-4612-0013-0_7.

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Kulp, Christopher W., and Vasilis Pagonis. "Lagrangian and Hamiltonian Dynamics." In Classical Mechanics, 229–72. Boca Raton : CRC Press, 2020.: CRC Press, 2020. http://dx.doi.org/10.1201/9781351024389-8.

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Kelley, J. Daniel, and Jacob J. Leventhal. "Lagrangian and Hamiltonian Dynamics." In Problems in Classical and Quantum Mechanics, 25–66. Cham: Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-46664-4_2.

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Trump, M. A., and W. C. Schieve. "The Lagrangian-Hamiltonian Theory." In Classical Relativistic Many-Body Dynamics, 121–86. Dordrecht: Springer Netherlands, 1999. http://dx.doi.org/10.1007/978-94-015-9303-8_5.

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Lewis, Debra. "Linearized Dynamics of Symmetric Lagrangian Systems." In Hamiltonian Dynamical Systems, 195–216. New York, NY: Springer New York, 1995. http://dx.doi.org/10.1007/978-1-4613-8448-9_14.

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Lee, Taeyoung, Melvin Leok, and N. Harris McClamroch. "Classical Lagrangian and Hamiltonian Dynamics." In Global Formulations of Lagrangian and Hamiltonian Dynamics on Manifolds, 89–129. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-56953-6_3.

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Lee, Taeyoung, Melvin Leok, and N. Harris McClamroch. "Lagrangian and Hamiltonian Dynamics on Manifolds." In Global Formulations of Lagrangian and Hamiltonian Dynamics on Manifolds, 347–98. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-56953-6_8.

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Lee, Taeyoung, Melvin Leok, and N. Harris McClamroch. "Lagrangian and Hamiltonian Dynamics on $$\mathsf{SO(3)}$$." In Global Formulations of Lagrangian and Hamiltonian Dynamics on Manifolds, 273–311. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-56953-6_6.

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Lee, Taeyoung, Melvin Leok, and N. Harris McClamroch. "Lagrangian and Hamiltonian Dynamics on $$\mathsf{SE(3)}$$." In Global Formulations of Lagrangian and Hamiltonian Dynamics on Manifolds, 313–46. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-56953-6_7.

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Lee, Taeyoung, Melvin Leok, and N. Harris McClamroch. "Lagrangian and Hamiltonian Dynamics on $$(\mathsf{S}^{1})^{n}$$." In Global Formulations of Lagrangian and Hamiltonian Dynamics on Manifolds, 131–206. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-56953-6_4.

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Conference papers on the topic "Hamiltonian and Lagrangian dynamics"

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Vontobel, Pascal O. "A factor-graph approach to Lagrangian and Hamiltonian dynamics." In 2011 IEEE International Symposium on Information Theory - ISIT. IEEE, 2011. http://dx.doi.org/10.1109/isit.2011.6033945.

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Lee, T., M. Leok, and N. Harris McClamroch. "Global Formulations of Lagrangian and Hamiltonian Dynamics on Embedded Manifolds." In IMA Conference on Mathematics of Robotics. Institute of Mathematics and its Applications, 2015. http://dx.doi.org/10.19124/ima.2015.001.19.

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Baleanu, Dumitru, Sami I. Muslih, and Eqab M. Rabei. "On Fractional Hamilton Formulation Within Caputo Derivatives." In ASME 2007 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2007. http://dx.doi.org/10.1115/detc2007-34812.

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The fractional Lagrangian and Hamiltonian dynamics is an important issue in fractional calculus area. The classical dynamics can be reformulated in terms of fractional derivatives. The fractional variational principles produce fractional Euler-Lagrange equations and fractional Hamiltonian equations. The fractional dynamics strongly depends of the fractional integration by parts as well as the non-locality of the fractional derivatives. In this paper we present the fractional Hamilton formulation based on Caputo fractional derivatives. One example is treated in details to show the characteristics of the fractional dynamics.
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Ghosh, Bijoy K., Takafumi Oki, Sanath D. Kahagalage, and Indika Wijayasinghe. "Asymptotically Stabilizing Potential Control for the Eye Movement Dynamics." In ASME 2014 Dynamic Systems and Control Conference. American Society of Mechanical Engineers, 2014. http://dx.doi.org/10.1115/dscc2014-5864.

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In this paper, we analyze the problem of stabilizing a rotating eye movement control system satisfying the Listing’s constraint. The control system is described using a suitably defined Lagrangian and written in the corresponding Hamiltonian form. We introduce a damping control and show that this choice of control asymptotically stabilizes the equilibrium point of the dynamics, while driving the state to a point of minimum total energy. The equilibrium point can be placed by appropriately locating the minimum of a potential function. The damping controller has been shown to be optimal with respect to a suitable cost function. We choose alternate forms of this cost function, by adding a term proportional to the potential energy, and synthesize stabilizing control, using numerical solution to the the well known Hamilton Jacobi Bellman equation. Using Chebyshev collocation method, the newly synthesized controller is compared with the damping control.
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Rastogi, Vikas, Amalendu Mukherjee, and Anirvan Dasgupta. "Extended Lagrangian Formalism and Invariants of Motion of Dynamical Systems: A Case Study of Electromechanical System." In ASME 2005 International Mechanical Engineering Congress and Exposition. ASMEDC, 2005. http://dx.doi.org/10.1115/imece2005-79113.

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In this paper, an extended Lagrangian formalism for general class of dynamical systems with dissipative, non-potential fields is formulated with the aim to obtain invariants of motion for such systems. A new concept of umbra-time has been introduced for this extension. D’Alembert basic idea of allowing displacement, when the real time is frozen is conveniently expressed in the terms of umbra-time. This leads to a peculiar form of equations, which is termed as umbra-Lagrange’s equations. A variational or least action doctrine leading to the proposed form of equation is introduced, which is based on recursive minimization of functionals. The concept of umbra-time extends the classical manifold over which the system evolves. The extension of Noether’s theorem in this extended space has been presented. The idea of umbra time is then used to propose the concept of umbra-Hamiltonian, which is used along with the extended Noether’s theorem to get into the dynamics of the dynamical systems with symmetries. In the mathematical models of dynamical system, the equations for the system can be formulated in a systematic way from the bondgraph representation as bondgraph representation of a system may be constructed in a total abstraction from the mathematical models of the dynamical system. In present paper, bond graphs are conveniently used to arrive at umbra-Lagrangian of the system. As a case study, we present a dynamic analysis of an electro-mechanical system through the proposed extended Lagrangian Formulation. The major objective of this paper is an analysis of symmetries of an electro-mechanical system comprising of an externally and internally damped, symmetric, elastic rotor driven by a three-phase induction motor, for which the umbra-Lagrangian remains unchanged under two families of transformations. The behaviour of limiting dynamics is obtained and validated through simulation studies.
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Spyrakos-Papastavridis, Emmanouil, Gustavo Medrano-Cerda, Jian S. Dai, and Darwin G. Caldwell. "Global Stability Study of a Compliant Double-Inverted Pendulum Based on Hamiltonian Modeling." In ASME 2012 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2012. http://dx.doi.org/10.1115/detc2012-71066.

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This paper presents a dynamical model of a compliant double-inverted pendulum that is used to approximate the physical structure of the compliant humanoid (COMAN) robot, using both the Hamiltonian and the Lagrangian approaches. A comparison between the two aims at providing insight into the various advantages and/or disadvantages associated to each approach. Through manipulation of the resulting formulae, it is shown that the Hamiltonian equations possess certain characteristics, such as the allowance of the tracking of global stability, that render this method of representation suitable for legged robotics applications. Finally, an asymptotically stabilizing control scheme is presented together with simulation results.
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SHESTAKOVA, TATYANA P. "HAMILTONIAN DYNAMICS IN EXTENDED PHASE SPACE FOR GRAVITY AND ITS CONSISTENCY WITH LAGRANGIAN FORMALISM: A GENERALIZED SPHERICALLY SYMMETRIC MODEL AS AN EXAMPLE." In Proceedings of the MG13 Meeting on General Relativity. WORLD SCIENTIFIC, 2015. http://dx.doi.org/10.1142/9789814623995_0305.

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Darrall, Bradley T., and Gary F. Dargush. "Mixed Convolved Action Principles for Dynamics of Linear Poroelastic Continua." In ASME 2015 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2015. http://dx.doi.org/10.1115/imece2015-52728.

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Although Lagrangian and Hamiltonian analytical mechanics represent perhaps the most remarkable expressions of the dynamics of a mechanical system, these approaches also come with limitations. In particular, there is inherent difficulty to represent dissipative processes and the restrictions placed on end point variations are not consistent with the definition of initial value problems. The present work on poroelastic media extends the recent formulation of a mixed convolved action to address a continuum dynamical problem with dissipation through the development of a new variational approach. The action in this proposed approach is formed by replacing the inner product in Hamilton’s principle with a time convolution. As a result, dissipative processes can be represented in a natural way and the required constraints on the variations are consistent with the actual initial and boundary conditions of the problem. The variational formulations developed here employ temporal impulses of velocity, effective stress, pore pressure and pore fluid mass flux as primary variables in this mixed approach, which also uses convolution operators and fractional calculus to achieve the desired characteristics. The resulting mixed convolved action is formulated in both the time and frequency domains to develop two new stationary principles for dynamic poroelasticity. In addition, the first variation of the action provides a temporally well-balanced weak form that leads to a new family of finite element methods in time, as well as space.
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CHIANG, R. "CONSTRUCTION OF LAGRANGIAN EMBEDDINGS USING HAMILTONIAN ACTIONS." In Proceedings of the COE International Workshop. WORLD SCIENTIFIC, 2005. http://dx.doi.org/10.1142/9789812775061_0007.

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Symon, Keith. "Applied Hamiltonian dynamics." In The Physics of Particle Accelerators Vol. I (based on the US Particle Accelerator School (USPAS) Seminars and Courses). AIP, 1992. http://dx.doi.org/10.1063/1.41999.

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Reports on the topic "Hamiltonian and Lagrangian dynamics"

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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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Wong, Michael K. W., and Edward Love. Lagrangian continuum dynamics in ALEGRA. Office of Scientific and Technical Information (OSTI), December 2007. http://dx.doi.org/10.2172/934850.

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Kyuldjiev, Assen, Vladimir Gerdjikov, and Giuseppe Marmo. Real Forms of Complexified Hamiltonian Dynamics. GIQ, 2012. http://dx.doi.org/10.7546/giq-3-2002-318-327.

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Hill, Ryan, Mikhail Shashkov, and Andrew Barlow. Interface-aware sub-scale dynamics closure model for multimaterial cells in Lagrangian gas dynamics. Office of Scientific and Technical Information (OSTI), February 2012. http://dx.doi.org/10.2172/1159556.

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Wang, L. S., P. S. Krishnaprasad, and J. H. Maddocks. Hamiltonian Dynamics of a Rigid Body in a Central Gravitational Field. Fort Belvoir, VA: Defense Technical Information Center, January 1990. http://dx.doi.org/10.21236/ada444554.

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Venturini, Marco. Stability Analysis of Longitudinal Beam Dynamics using Noncanonical Hamiltonian Methods and Energy Principles. Office of Scientific and Technical Information (OSTI), August 2002. http://dx.doi.org/10.2172/799993.

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Knobloch, Edgar, and Jerrold E. Marsden. Bifurcation, Geometric Phases and Control in Hamiltonian Systems and Fluid Dynamics. Final report. Office of Scientific and Technical Information (OSTI), July 2000. http://dx.doi.org/10.2172/763415.

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Abarbanel, Henry D., and Ali Rouhi. Hamiltonian Dynamics of Coupled Potential Vorticity and Internal Wave Motion: 1. Linear Modes. Fort Belvoir, VA: Defense Technical Information Center, February 1993. http://dx.doi.org/10.21236/ada263469.

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Kadtke, James B. Investigations of Equilibria, Lattices, and Chatoic Dynamics of 2-D hamiltonian Point Vortices. Fort Belvoir, VA: Defense Technical Information Center, August 1990. http://dx.doi.org/10.21236/ada227364.

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