Relevant bibliographies by topics / Lagrangian coordinates

Contents

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

Academic literature on the topic 'Lagrangian coordinates'

Author: Grafiati
Published: 4 June 2021
Last updated: 20 June 2025

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Journal articles on the topic "Lagrangian coordinates"

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CAPOZZIELLO, SALVATORE, and RUGGIERO DE RITIS. "SCALE FACTOR DUALITY AND GENERAL TRANSFORMATIONS FOR STRING COSMOLOGY." International Journal of Modern Physics D 02, no. 03 (1993): 367–71. http://dx.doi.org/10.1142/s0218271893000258.

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We adopt a general point of view to obtain the scale factor duality for a class of nonminimally coupled gravitational Lagrangians which comprises the tree-level effective Lagrangian of string-dilaton cosmology. We show that in a new system of coordinates the duality is a reflection and the Lagrangians become cyclic with respect to a coordinate. When this is the situation, the dynamics is simplified and it is easier to obtain exact solutions.
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Abrashkin, Anatoly, and Efim Pelinovsky. "Lagrange form of the nonlinear Schrödinger equation for low-vorticity waves in deep water." Nonlinear Processes in Geophysics 24, no. 2 (2017): 255–64. http://dx.doi.org/10.5194/npg-24-255-2017.

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Abstract. The nonlinear Schrödinger (NLS) equation describing the propagation of weakly rotational wave packets in an infinitely deep fluid in Lagrangian coordinates has been derived. The vorticity is assumed to be an arbitrary function of Lagrangian coordinates and quadratic in the small parameter proportional to the wave steepness. The vorticity effects manifest themselves in a shift of the wave number in the carrier wave and in variation in the coefficient multiplying the nonlinear term. In the case of vorticity dependence on the vertical Lagrangian coordinate only (Gouyon waves), the shift of the wave number and the respective coefficient are constant. When the vorticity is dependent on both Lagrangian coordinates, the shift of the wave number is horizontally inhomogeneous. There are special cases (e.g., Gerstner waves) in which the vorticity is proportional to the squared wave amplitude and nonlinearity disappears, thus making the equations for wave packet dynamics linear. It is shown that the NLS solution for weakly rotational waves in the Eulerian variables may be obtained from the Lagrangian solution by simply changing the horizontal coordinates.
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Qian, Yu-Kun, Shiqiu Peng, and Chang-Xia Liang. "Reconciling Lagrangian Diffusivity and Effective Diffusivity in Contour-Based Coordinates." Journal of Physical Oceanography 49, no. 6 (2019): 1521–39. http://dx.doi.org/10.1175/jpo-d-18-0251.1.

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AbstractThe present study reconciles theoretical differences between the Lagrangian diffusivity and effective diffusivity in a transformed spatial coordinate based on the contours of a quasi-conservative tracer. In the transformed coordinate, any adiabatic stirring effect, such as shear-induced dispersion, is naturally isolated from diabatic cross-contour motions. Therefore, Lagrangian particle motions in the transformed coordinate obey a transformed zeroth-order stochastic (i.e., random walk) model with the diffusivity replaced by the effective diffusivity. Such a stochastic model becomes the theoretical foundation on which both diffusivities are exactly unified. In the absence of small-scale diffusion, particles do not disperse at all in the transformed contour coordinate. Besides, the corresponding Lagrangian autocorrelation becomes a delta function and is thus free from pronounced overshoot and negative lobe at short time lags that may be induced by either Rossby waves or mesoscale eddies; that is, particles decorrelate immediately and Lagrangian diffusivity is already asymptotic no matter how small the time lag is. The resulting instantaneous Lagrangian spreading rate is thus conceptually identical to the effective diffusivity that only measures the instantaneous irreversible mixing. In these regards, the present study provides a new look at particle dispersion in contour-based coordinates.
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Thiffeault, Jean-Luc. "Advection–diffusion in Lagrangian coordinates." Physics Letters A 309, no. 5-6 (2003): 415–22. http://dx.doi.org/10.1016/s0375-9601(03)00244-5.

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Brown, J. David. "Singular Lagrangians and the Dirac–Bergmann algorithm in classical mechanics." American Journal of Physics 91, no. 3 (2023): 214–24. http://dx.doi.org/10.1119/5.0107540.

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Textbook treatments of classical mechanics typically assume that the Lagrangian is nonsingular; that is, the matrix of second derivatives of the Lagrangian with respect to the velocities is invertible. This assumption ensures that (i) Lagrange's equations can be solved for the accelerations as functions of coordinates and velocities, and (ii) the definitions of the conjugate momenta can be inverted to solve for the velocities as functions of coordinates and momenta. This assumption, however, is unnecessarily restrictive—there are interesting classical dynamical systems with singular Lagrangians. The algorithm for analyzing such systems was developed by Dirac and Bergmann in the 1950s. After a brief review of the Dirac–Bergmann algorithm, several examples are presented using familiar components: point masses connected by massless springs, rods, cords, and pulleys.
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Kopiev, V. F., and S. A. Chernyshev. "LAGRANGIAN FORMALISM IN PROBLEMS OF SMALL OSCILLATIONS OF VORTEX FLOWS AND ITS CONNECTION WITH THE VARIATIONAL PRINCIPLE FOR IDEAL INCOMPRESSIBLE HYDRODYNAMICS OF VORTEX LINES." XXII workshop of the Council of nonlinear dynamics of the Russian Academy of Sciences 47, no. 1 (2019): 74–77. http://dx.doi.org/10.29006/1564-2291.jor-2019.47(1).21.

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The paper discusses the description of vortex flows of an ideal incompressible fluid based on the formalism of Lagrangian mechanics. Using the displacement field of liquid particles as a generalized coordinate, we write out the Lagrangian describing the dynamics of small perturbations (Kopiev, Chernyshev, 2018). The corresponding Lagrange equations are the equation for the displacement field (Drazim, Reid, 1981): This equation is equivalent to the Helmholtz equation for vorticity perturbations. The displacement field is defined as the difference in the positions of liquid particles on trajectories in disturbed and undisturbed flows. Although this definition is given in terms of Lagrangian variables associated with liquid particles, the displacement field itself is an Euler variable, expressed through velocity and vorticity perturbations. An example of using Lagrangian to solve the problem of conservation of the quadrupole moment of a vortex flow is considered. Using the Noether theorem, conditions on a stationary flow are obtained, under which the quadrupole moment of small perturbations of this flow is an integral of motion (Kopiev, Chernyshev, 2018). It is shown that these conditions are satisfied for the jet flows uniform along the longitudinal coordinate. The result obtained is important in aeroacoustics due to the fact that the quadrupole moment of the vortex flow represents the main term of the decomposition of a compact acoustic source in Machnumber (Lighthill, 1952; Crow, 1970; Kopiev, Chernyshev, 1995). The generalization of these results to the nonlinear case is considered. The Lagrangian is obtained for an arbitrary nonlinear displacement field: nowhere Gis Green’s function of the Laplace equation. The corresponding Lagrange equations coincide with the differential equations describing the nonlinear dynamics of the displacement field (Drazin, Reid, 1981). Expansion of the Lagrangian in small perturbations to quadratic terms gives the Lagrangian of the linear system. The question of the relationship of the proposed approach to the description of the dynamics of an incompressible fluid and known approaches based on the formalism of Lagrangian mechanics with the coordinates of liquid particles as generalized coordinates (Chapman, 1978; Goncharov, Pavlov, 2008; Kuznetsov, Ruban, 1998) is considered. It is shown that the transformation of the Lagrangian obtained in (Kuznetsov, Ruban, 1998) to the Lagrangian can be carried out by transforming Lagrangian variables (coordinates of liquid particles) to Eulerian variables (displacement field). This study was supported by the Russian Science Foundation, project No. 17-11-01271.
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Meleshko, Sergey V., and Evgeniy I. Kaptsov. "Symmetry Analysis of the Two-Dimensional Stationary Gas Dynamics Equations in Lagrangian Coordinates." Mathematics 12, no. 6 (2024): 879. http://dx.doi.org/10.3390/math12060879.

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This article analyzes the symmetry of two-dimensional stationary gas dynamics equations in Lagrangian coordinates, including the search for equivalence transformations, the group classification of equations, the derivation of group foliations, and the construction of conservation laws. The consideration of equations in Lagrangian coordinates significantly simplifies the procedure for obtaining conservation laws, which are derived using the Noether theorem. The final part of the work is devoted to group foliations of the gas dynamics equations, including for the nonstationary isentropic case. The group foliations approach is usually employed for equations that admit infinite-dimensional groups of transformations (which is exactly the case for the gas dynamics equations in Lagrangian coordinates) and may make it possible to simplify their further analysis. The results obtained in this regard generalize previously known results for the two-dimensional shallow water equations in Lagrangian coordinates.
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Thiffeault, Jean-Luc. "The strange eigenmode in Lagrangian coordinates." Chaos: An Interdisciplinary Journal of Nonlinear Science 14, no. 3 (2004): 531–38. http://dx.doi.org/10.1063/1.1759431.

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Dubos, Thomas, and Marine Tort. "Equations of Atmospheric Motion in Non-Eulerian Vertical Coordinates: Vector-Invariant Form and Quasi-Hamiltonian Formulation." Monthly Weather Review 142, no. 10 (2014): 3860–80. http://dx.doi.org/10.1175/mwr-d-14-00069.1.

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Abstract The curl form of equations of inviscid atmospheric motion in general non-Eulerian coordinates is obtained. Narrowing down to a general vertical coordinate, a quasi-Hamiltonian form is then obtained in a Lagrangian, isentropic, mass-based or z-based vertical coordinate. In non-Lagrangian vertical coordinates, the conservation of energy by the vertical transport terms results from the invariance of energy under the vertical relabeling of fluid parcels. A complete or partial separation between the horizontal and vertical dynamics is achieved, except in the Eulerian case. The horizontal–vertical separation is especially helpful for (quasi-)hydrostatic systems characterized by vanishing vertical momentum. Indeed for such systems vertical momentum balance reduces to a simple statement: total energy is stationary with respect to adiabatic vertical displacements of fluid parcels. From this point of view the purpose of (quasi-)hydrostatic balance is to determine the vertical positions of fluid parcels, for which no evolution equation is readily available. This physically appealing formulation significantly extends previous work. The general formalism is exemplified for the fully compressible Euler equations in a Lagrangian vertical coordinate and a Cartesian (x, z) slice geometry, and the deep-atmosphere quasi-hydrostatic equations in latitude–longitude horizontal coordinates. The latter case, in particular, illuminates how the apparent intricacy of the time-dependent metric terms and of the additional forces can be absorbed into a proper choice of prognostic variables. In both cases it is shown how the quasi-Hamiltonian form leads straightforwardly to the conservation of energy using only integration by parts. Relationships with previous work and implications for stability analysis and the derivation of approximate sets of equations and energy-conserving numerical schemes are discussed.
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Bleck, Rainer, Stan Benjamin, Jin Lee, and Alexander E. MacDonald. "On the Use of an Adaptive, Hybrid-Isentropic Vertical Coordinate in Global Atmospheric Modeling." Monthly Weather Review 138, no. 6 (2010): 2188–210. http://dx.doi.org/10.1175/2009mwr3103.1.

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Abstract This article is one in a series describing the functionality of the Flow-Following, Finite-Volume Icosahedral Model (FIM) developed at NOAA’s Earth System Research Laboratory. Emphasis in this article is on the design of the vertical coordinate—the “flow following” aspect of FIM. The coordinate is terrain-following near the ground and isentropic in the free atmosphere. The spatial transition between the two coordinates is adaptive and is based on the arbitrary Lagrangian–Eulerian (ALE) paradigm. The impact of vertical resolution trade-offs between the present hybrid approach and traditional terrain-following coordinates is demonstrated in a three-part case study.
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Dissertations / Theses on the topic "Lagrangian coordinates"

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Wang, Xiaojun. "Well-posedness results for a class of complex flow problems in the high Weissenberg number limit." Diss., Virginia Tech, 2012. http://hdl.handle.net/10919/27669.

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For simple fluids, or Newtonian fluids, the study of the Navier-Stokes equations in the high Reynolds number limit brings about two fundamental research subjects, the Euler equations and the Prandtl's system. The consideration of infinite Reynolds number reduces the Navier-Stokes equations to the Euler equations, both of which are dealing with the entire flow region. Prandtl's system consists of the governing equations of the boundary layer, a thin layer formed at the wall boundary where viscosity cannot be neglected. In this dissertation, we investigate the upper convected Maxwell(UCM) model for complex fluids, or non-Newtonian fluids, in the high Weissenberg number limit. This is analogous to the Newtonian fluids in the high Reynolds number limit. We present two well-posedness results. The first result is on an initial-boundary value problem for incompressible hypoelastic materials which arise as a high Weissenberg number limit of viscoelastic fluids. We first assume the stress tensor is rank-one and develop energy estimates to show the problem is locally well-posed. Then we show the more general case can be handled in the same spirit. This problem is closely related to the incompressible ideal magneto-hydrodynamics (MHD) system. The second result addresses the formulation of a time-dependent elastic boundary layer through scaling analysis. We show the well-posedness of this boundary layer by transforming to Lagrangian coordinates. In contrast to the possible ill-posedness of Prandtl's system in Newtonian fluids, we prove that in non-Newtonian fluids the stress boundary layer problem is well-posed.<br>Ph. D.
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Beltran, Royo César. "Generalized unit commitment by the radar multiplier method." Doctoral thesis, Universitat Politècnica de Catalunya, 2001. http://hdl.handle.net/10803/6501.

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This operations research thesis should be situated in the field of the power generation industry. The general objective of this work is to efficiently solve the Generalized Unit Commitment (GUC) problem by means of specialized software. The GUC problem generalizes the Unit Commitment (UC) problem by simultane-ously solving the associated Optimal Power Flow (OPF) problem. There are many approaches to solve the UC and OPF problems separately, but approaches to solve them jointly, i.e. to solve the GUC problem, are quite scarce. One of these GUC solving approaches is due to professors Batut and Renaud, whose methodology has been taken as a starting point for the methodology presented herein.<br/>This thesis report is structured as follows. Chapter 1 describes the state of the art of the UC and GUC problems. The formulation of the classical short-term power planning problems related to the GUC problem, namely the economic dispatching problem, the OPF problem, and the UC problem, are reviewed. Special attention is paid to the UC literature and to the traditional methods for solving the UC problem. In chapter 2 we extend the OPF model developed by professors Heredia and Nabona to obtain our GUC model. The variables used and the modelling of the thermal, hydraulic and transmission systems are introduced, as is the objective function. Chapter 3 deals with the Variable Duplication (VD) method, which is used to decompose the GUC problem as an alternative to the Classical Lagrangian Relaxation (CLR) method. Furthermore, in chapter 3 dual bounds provided by the VDmethod or by the CLR methods are theoretically compared.<br/>Throughout chapters 4, 5, and 6 our solution methodology, the Radar Multiplier (RM) method, is designed and tested. Three independent matters are studied: first, the auxiliary problem principle method, used by Batut and Renaud to treat the inseparable augmented Lagrangian, is compared with the block coordinate descent method from both theoretical and practical points of view. Second, the Radar Sub- gradient (RS) method, a new Lagrange multiplier updating method, is proposed and computationally compared with the classical subgradient method. And third, we study the local character of the optimizers computed by the Augmented Lagrangian Relaxation (ALR) method when solving the GUC problem. A heuristic to improve the local ALR optimizers is designed and tested.<br/>Chapter 7 is devoted to our computational implementation of the RM method, the MACH code. First, the design of MACH is reviewed brie y and then its performance is tested by solving real-life large-scale UC and GUC instances. Solutions computed using our VD formulation of the GUC problem are partially primal feasible since they do not necessarily fulfill the spinning reserve constraints. In chapter 8 we study how to modify this GUC formulation with the aim of obtaining full primal feasible solutions. A successful test based on a simple UC problem is reported. The conclusions, contributions of the thesis, and proposed further research can be found in chapter 9.
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Books on the topic "Lagrangian coordinates"

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Meĭrmanov, A. M. Evolution equations and Lagrangian coordinates. Walter de Gruyter, 1997.

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Pukhnachov, Vladislav V., Sergei I. Shmarev, and Anvarbek M. Meirmanov. Evolution Equations and Lagrangian Coordinates. de Gruyter GmbH, Walter, 2011.

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Evolution Equations and Lagrangian Coordinates. De Gruyter, Inc., 1997.

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Mann, Peter. Point Transformations in Lagrangian Mechanics. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198822370.003.0009.

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This chapter discusses point transformations in Lagrangian mechanics. Sometimes, when solving problems, it is useful to change coordinates in velocity phase space to better suit and simplify the system at hand; this is a requirement of any physical theory. This change is often motivated by some experimentally observed physicality of the system or may highlight new conserved quantities that might have been overlooked using the old description. In the Newtonian formalism, it was a bit of a hassle to change coordinates and the equations of motion will look quite different. In this chapter, point transformations in Lagrangian mechanics are developed and the Euler–Lagrange equation is found to be covariant. The chapter discusses coordinate transformations, parametrisation invariance and the Jacobian of the transform. Re-parametrisations are also included.
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Coopersmith, Jennifer. Lagrangian Mechanics. Oxford University Press, 2017. http://dx.doi.org/10.1093/oso/9780198743040.003.0006.

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It is demonstrated how d’Alembert’s Principle can be used as the basis for a more general mechanics – Lagrangian Mechanics. How this leads to Hamilton’s Principle (the Principle of Least Action) is shown mathematically and in words. It is further explained why Lagrangian Mechanics is so general, why forces of constraint may be ignored, and how external conditions lead to “curved space.” Also, it is explained why the Lagrangian, L, has the form L = T − V (where T is the kinetic energy and V is the potential energy), and why T is in “quadratic form” (T = 1/2mv2). It is shown how Noether’s Theorem leads to a more fundamental definition of energy and links the conservation of energy to the homogeneity of time. The ingenious Lagrange multipliers are explained, and also generalized forces and generalized coordinates.
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Mann, Peter. Constrained Lagrangian Mechanics. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198822370.003.0008.

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This chapter builds on the previous two chapters to tackle constrained systems, using Lagrangian mechanics and constrained variations. The first section deals with holonomic constraint equations using Lagrange multipliers; these can be used to reduce the number of coordinates until a linearly independent minimal set is obtained that describes a constraint surface within configuration space, so that Lagrange equations can be set up and solved. Motion is understood to be confined to a constraint submanifold. The variational formulation of non-holonomic constraints is then discussed to derive the vakonomic formulation. These erroneous equations are then compared to the central Lagrange equation, and the precise nature of the variations used in each formulation is investigated. The vakonomic equations are then presented in their Suslov form (Suslov–vakonomic form) in an attempt to reconcile the two approaches. In addition, the structure of biological membranes is framed as a constrained optimisation problem.
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Mann, Peter. Coordinates & Constraints. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198822370.003.0006.

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This short chapter introduces constraints, generalised coordinates and the various spaces of Lagrangian mechanics. Analytical mechanics concerns itself with scalar quantities of a dynamic system, namely the potential and kinetic energies of the particle; this approach is in opposition to Newton’s method of vectorial mechanics, which relies upon defining the position of the particle in three-dimensional space, and the forces acting upon it. The chapter serves as an informal, non-mathematical introduction to differential geometry concepts that describe the configuration space and velocity phase space as a manifold and a tangent, respectively. The distinction between holonomic and non-holonomic constraints is discussed, as are isoperimetric constraints, configuration manifolds, generalised velocity and tangent bundles. The chapter also introduces constraint submanifolds, in an intuitive, graphic format.
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Mann, Peter. Symmetries & Lagrangian-Hamilton-Jacobi Theory. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198822370.003.0011.

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This chapter discusses conservation laws in Lagrangian mechanics and shows that certain conservation laws are just particular examples of a more fundamental theory called ‘Noether’s theorem’, after Amalie ‘Emmy’ Noether, who first discovered it in 1918. The chapter starts off by discussing Noether’s theorem and symmetry transformations in Lagrangian mechanics in detail. It then moves on to gauge theory and surface terms in the action before isotropic symmetries. continuous symmetry, conserved quantities, conjugate momentum, cyclic coordinates, Hessian condition and discrete symmetries are discussed. The chapter also covers Lie algebra, spontaneous symmetry breaking, reduction theorems, non-dynamical symmetries and Ostrogradsky momentum. The final section of the chapter details Carathéodory–Hamilton–Jacobi theory in the Lagrangian setting, to derive the Hamilton–Jacobi equation on the tangent bundle!
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Mann, Peter. The Jacobi Energy Function. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198822370.003.0010.

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This chapter focuses on the Jacobi energy function, considering how the Lagrange formalism treats the energy of the system. This discussion leads nicely to conservation laws and symmetries, which are the focus of the next chapter. The Jacobi energy function associated with a Lagrangian is defined as a function on the tangent bundle. The chapter also discuss explicit vs implicit time dependence, and shows how time translational invariance ensures the generalised coordinates are inertial, meaning that the energy function is the total energy of the system. In addition, it examines the energy function using non-inertial coordinates and explicit time dependence.
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Mann, Peter. Near-Integrable Systems. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198822370.003.0024.

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This chapter extends the now familiar Lagrangian formulation to a field theory and covers elementary material in this new setting. The motion of systems with a very large number of degrees of freedom makes it necessary to specify an almost infinite number of discrete coordinates. It is possible to simplify the situation by taking the continuum limit, which replaces the individual coordinates with a continuous function that describes a displacement field, which assigns a displacement vector to each position the system could occupy relative to an equilibrium configuration. The field thus takes a point in the spacetime manifold and assigns it a value corresponding to whatever the field represents. In this chapter, many interdisciplinary examples are solved and pedagogical models are discussed. The chapter also discusses Lagrange density, the Lagrange field equation, instantons, the Klein–Gordon equation, Fourier transforms and the Korteweg–de Vries equation.
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Book chapters on the topic "Lagrangian coordinates"

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DiBenedetto, Emmanuele. "Constraints and Lagrangian Coordinates." In Classical Mechanics. Birkhäuser Boston, 2010. http://dx.doi.org/10.1007/978-0-8176-4648-6_2.

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Pila, Aron Wolf. "Quasi-Coordinates and Quasi-Velocities." In Introduction To Lagrangian Dynamics. Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-22378-6_4.

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Hui, Wai-How, and Kun Xu. "Lagrangian Gas Dynamics." In Computational Fluid Dynamics Based on the Unified Coordinates. Springer Berlin Heidelberg, 2012. http://dx.doi.org/10.1007/978-3-642-25896-1_8.

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Ludovic, L., C. Estelle, and L. Jorge. "The Lagrangian Coordinates Applied to the LWR Model." In Hyperbolic Problems: Theory, Numerics, Applications. Springer Berlin Heidelberg, 2008. http://dx.doi.org/10.1007/978-3-540-75712-2_67.

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Weinstock, J. "Lagrangian Coordinates and their Application to Gravity Wave Spectra." In Coupling Processes in the Lower and Middle Atmosphere. Springer Netherlands, 1993. http://dx.doi.org/10.1007/978-94-011-1594-0_17.

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Chalons, Christophe, Régis Duvigneau, and Camilla Fiorini. "Sensitivity Analysis for the Euler Equations in Lagrangian Coordinates." In Springer Proceedings in Mathematics & Statistics. Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-57394-6_8.

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Podder, Debabrata, and Santanu Chatterjee. "Basic Concepts of Generalized Coordinates, Lagrangian, and Hamiltonian Mechanics." In Introduction to Structural Analysis. CRC Press, 2021. http://dx.doi.org/10.1201/9781003081227-6.

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Forbes, Jerry W. "Special Topics: Lagrangian Coordinates, Spall, and Radiation Induced Shocks." In Shock Wave Compression of Condensed Matter. Springer Berlin Heidelberg, 2012. http://dx.doi.org/10.1007/978-3-642-32535-9_11.

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Armenio, Vincenzo, Ugo Piomelli, and Virgilio Fiorotto. "Applications of a Lagrangian Mixed SGS Model in Generalized Coordinates." In Direct and Large-Eddy Simulation III. Springer Netherlands, 1999. http://dx.doi.org/10.1007/978-94-015-9285-7_12.

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Wagner, David H. "The transformation from Eulerian to Lagrangian coordinates for solutions with discontinuities." In Lecture Notes in Mathematics. Springer Berlin Heidelberg, 1987. http://dx.doi.org/10.1007/bfb0078327.

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Conference papers on the topic "Lagrangian coordinates"

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BOILLAT, GUY, and YUE-JUN PENG. "LINEARIZED EULER'S VARIATIONAL EQUATIONS IN LAGRANGIAN COORDINATES." In Proceedings of the 14th Conference on WASCOM 2007. WORLD SCIENTIFIC, 2008. http://dx.doi.org/10.1142/9789812772350_0008.

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Kaewmanee, Chompit, and Sergey V. Meleshko. "Symmetries of one-dimensional fluid equations in Lagrangian coordinates." In MODERN TREATMENT OF SYMMETRIES, DIFFERENTIAL EQUATIONS AND APPLICATIONS (Symmetry 2019). AIP Publishing, 2019. http://dx.doi.org/10.1063/1.5125073.

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Shmarev, Sergei I. "Lagrangian coordinates in free boundary problems for multidimensional parabolic equations." In Proceedings of the 4th European Conference. WORLD SCIENTIFIC, 2002. http://dx.doi.org/10.1142/9789812777201_0026.

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Park, J. H., J. H. Choi, and D. S. Bae. "A Relative Nodal Coordinate Formulation for Finite Element Nonlinear Analysis." 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-21315.

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Abstract Nodal coordinates are referred to a fixed configuration in the conventional equations of equilibrium. Nodal coordinates are referred to the initial configuration in the total Lagrangian formulation and to the last calculated configuration in the updated Lagrangian formulation. This research proposes to use the relative nodal coordinates in representing the position and orientation for a node. Since the nodal coordinates are measured relative to its adjacent nodal reference frame, they are still small for a structure undergoing large deformations if the element sizes are small. As a consequence, many element formulations developed under small deformation assumptions are still valid for structures undergoing large deformations, which significantly simplifies the equations of equilibrium. A structural system is represented by a graph to systematically develop the governing equations of equilibrium for general systems. A node and an element are represented by a node and an edge in graph form, respectively. Closed loops are opened to form a tree topology by cutting edges. Two computational sequences are defined in a graph. One is the forward path sequence that is used to recover the Cartesian nodal deformations from relative nodal displacements and traverses a graph from the base node towards the terminal nodes. The other is the backward path sequence that is used to recover the nodal forces in the relative coordinate system from the known nodal forces in the absolute coordinate system and traverses from the terminal nodes towards the base node. One open loop and one closed loop structure undergoing large displacements are analyzed to demonstrate the efficiency and validity of the proposed method.
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Liu, Xiaodong, Nathaniel R. Morgan, and Donald E. Burton. "A Lagrangian discontinuous Galerkin hydrodynamic method for 2D Cartesian and RZ axisymmetric coordinates." In 2018 AIAA Aerospace Sciences Meeting. American Institute of Aeronautics and Astronautics, 2018. http://dx.doi.org/10.2514/6.2018-1562.

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Kaptsov, Evgeniy I., and Sergey V. Meleshko. "Conservation laws of the one-dimensional isentropic gas dynamics equations in Lagrangian coordinates." In MODERN TREATMENT OF SYMMETRIES, DIFFERENTIAL EQUATIONS AND APPLICATIONS (Symmetry 2019). AIP Publishing, 2019. http://dx.doi.org/10.1063/1.5125074.

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Orzechowski, Grzegorz, Aki M. Mikkola, and José L. Escalona. "Co-Simulation Procedure for Multibody Reeving Systems." In ASME 2018 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2018. http://dx.doi.org/10.1115/detc2018-86422.

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In this paper, co-simulation procedure for a multibody system that includes reeving mechanism will be introduced. The multibody system under investigation is assumed to have a set of rigid bodies connected by flexible wire ropes using a set of sheaves and reels. In the co-simulation procedure, a wire rope is described using a combination of absolute position coordinates, relative transverse deformation coordinates and longitudinal material coordinates. Accordingly, each wire rope span is modeled using a single two-noded element by employing an Arbitrary Lagrangian-Eulerian approach.
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8

Ebna Hai, Bhuiyan Shameem Mahmood, and Markus Bause. "Finite Element Approximation of Fluid Structure Interaction (FSI) Optimization in Arbitrary Lagrangian-Eulerian Coordinates." In ASME 2013 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2013. http://dx.doi.org/10.1115/imece2013-62291.

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Advanced composite materials such as Carbon Fiber Reinforced Plastics (CFRP) are being applied to many aircraft structures in order to improve performance and reduce weight. Most composites have strong, stiff fibers in a matrix which is weaker and less stiff. However, aircraft wings can break due to Fluid-Structure Interaction (FSI) oscillations or material fatigue. This paper focuses on the analysis of a non-linear fluid-structure interaction problem and its solution in the finite element software package DOpElib: the deal.II based optimization library. The principal aim of this research is to explore and understand the behaviour of the fluid-structure interaction during the impact of a deformable material (e.g. an aircraft wing) on air. Here we briefly describe the analysis of incompressible Navier-Stokes and Elastodynamic equations in the arbitrary Lagrangian-Eulerian (ALE) frameworks in order to numerically simulate the FSI effect on a double wedge airfoil. Since analytical solutions are only available in special cases, the equation needs to be solved by numerical methods. This coupled problem is defined in a monolithic framework and fractional-step-θ time stepping scheme are implemented. Spatial discretization is based on a Galerkin finite element scheme. The non-linear system is solved by a Newton method. The implementation using the software library package DOpElib and deal.II serves for the computation of different fluid-structure configurations.
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9

Tsirkunov, Yury M., Aleksei N. Volkov, and Natalia V. Tarasova. "Full Lagrangian Approach to the Calculation of Dilute Dispersed Phase Flows: Advantages and Applications." In ASME 2002 Joint U.S.-European Fluids Engineering Division Conference. ASMEDC, 2002. http://dx.doi.org/10.1115/fedsm2002-31224.

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An efficient numerical method developed recently in Russia for calculations of dilute particle phase flow fields in two-phase gas-particle flows is presented in this paper. The method is based on the full Lagrangian approach (FLA) to the description of the regular motion of the particle phase. The collisionless “gas” of particles is treated as a continuum for which all basic equations, namely, the continuity equation, the momentum equation and the energy equation are written in the Lagrangian coordinates. The traditional Lagrangian approach (LA) widely used in the West does not deal with the explicit form of the continuity equation for the particle phase, and this is the key difference between FLA and LA. The FLA-method has some advantages over the traditional Lagrangian technique. Examples of numerical calculations of two-phase flows with a complex particle phase flow structure illustrate this method.
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10

Mohammadi, Narges, and José Luis Escalona. "Dynamic Simulation of Reeving Systems With the Extension of the Modal Approach in the Axial Direction." In ASME 2021 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2021. http://dx.doi.org/10.1115/detc2021-71078.

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Abstract In this work, the simulation of reeving systems has been studied by including axial modes using the Arbitrary Lagrangian-Eulerian (ALE) description. The reeving system is considered as a deformable multibody system in which the rigid bodies are connected by the elastic wire ropes through sheaves and reels. A set of absolute nodal coordinates and modal coordinates is employed to describe the motion and deformation in the axial direction. This new method allows the analysis of elements with non-constant axial strain along its length. In addition, modal coordinates are employed to describe the dynamic motion in the transverse direction. The non-constant axial displacement within the wire rope is computed in terms of the absolute position coordinates, longitudinal material coordinates, and modal deformation coordinates. To derive the governing equations of motion, Lagrange’s equation is employed. The formulation is validated for a simple pendulumlike motion actuated by an initial velocity. The simulation results are provided to trace the movements of the payload. It can be seen that by adding modal coordinates, the axial force within the element changes. Moreover, the effects of modal coordinates in the axial direction are presented for a different number of nodes, and the resulting axial forces are compared with reference solution.
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