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Books on the topic 'Lagrangean approach'

Author: Grafiati

Published: 4 June 2021

Last updated: 17 February 2022

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1

Lee, J. H. W. Turbulent jets and plumes: A Lagrangian approach. Kluwer Academic Publishers, 2002.

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2

1942-, Chu Vincent H., ed. Turbulent jets and plumes: A Lagrangian approach. Kluwer Academic Publishers, 2003.

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3

1952-, Kunisch K., ed. Lagrange multiplier approach to variational problems and applications. Society for Industrial and Applied Mathematics, 2008.

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4

Misspecification tests in econometrics: The Lagrange multiplier principle and other approaches. Cambridge University Press, 1988.

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5

R, Rodrigues Paulo, ed. Generalized classical mechanics and field theory: A geometrical approach of Lagrangian and Hamiltonian formalisms involving higher order derivatives. North-Holland, 1985.

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6

Van, Anh Le, and Rabah Bouzidi. Lagrangian Mechanics: An Advanced Analytical Approach. Wiley & Sons, Incorporated, John, 2019.

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7

Van, Anh Le, and Rabah Bouzidi. Lagrangian Mechanics: An Advanced Analytical Approach. Wiley & Sons, Incorporated, John, 2019.

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8

Van, Anh Le, and Rabah Bouzidi. Lagrangian Mechanics: An Advanced Analytical Approach. Wiley & Sons, Incorporated, John, 2019.

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9

Lee, Joseph Hun-wei, and Vincent Chu. Turbulent Jets and Plumes: A Lagrangian Approach. Springer, 2003.

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10

Lagrangian Transport in Geophysical Jets and Waves: The Dynamical Systems Approach (Interdisciplinary Applied Mathematics). Springer, 2006.

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11

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

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12

Coupled Lagrangian and Eulerian Approach to Detonation and Fragmentation Problems. Storming Media, 2001.

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13

Feynman's thesis: A new approach to quantum theory. World Scientific, 2005.

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14

Feynman, Richard Phillips. Feynman's Thesis: A New Approach to Quantum Theory. World Scientific Publishing Company, 2005.

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15

Feynman, Richard Phillips. Feynman's Thesis: A New Approach to Quantum Theory. World Scientific Publishing Company, 2005.

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16

Chorlay, Renaud. Questions of generality as probes into nineteenth-century mathematical analysis. Edited by Karine Chemla, Renaud Chorlay, and David Rabouin. Oxford University Press, 2017. http://dx.doi.org/10.1093/oxfordhb/9780198777267.013.14.

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This article examines ways of expressing generality and epistemic configurations in which generality issues became intertwined with epistemological topics, such as rigor, or mathematical topics, such as point-set theory. In this regard, three very specific configurations are discussed: the first evolving from Niels Henrik Abel to Karl Weierstrass, the second in Joseph-Louis Lagrange’s treatises on analytic functions, and the third in Emile Borel. Using questions of generality, the article first compares two major treatises on function theory, one by Lagrange and one by Augustin Louis Cauchy. I

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17

Wiggins, Stephen, and Roger M. Samelson. Lagrangian Transport in Geophysical Jets and Waves: The Dynamical Systems Approach. Springer, 2010.

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18

Meng-Sing, Liou, Hindman Richard G, and United States. National Aeronautics and Space Administration., eds. An approach for dynamic grids. National Aeronautics and Space Administration, 1994.

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19

An approach for dynamic grids. National Aeronautics and Space Administration, 1994.

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20

Udaykumar, H. S. A mixed Eulerian-Lagrangian approach for the simulation of interfacial phenomena in solidifcation processing. 1994.

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21

Applications of Arbitrary Lagrangian Eulerian (ALE) Analysis Approach to Underwater and Air Explosion Problems. Storming Media, 2000.

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22

D, Salas M., and Institute for Computer Applications in Science and Engineering., eds. Lagrangian approach to jet mixing and optimization of the reactor for production of carbon nanotubes. ICASE, National Aeronautics and Space Administration, Langley Research Center, 2001.

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23

Global Formulations of Lagrangian and Hamiltonian Dynamics on Manifolds: A Geometric Approach to Modeling and Analysis. Springer, 2017.

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24

Finite element simulation of a space shuttle solid rocket booster aft skirt splashdown using an arbitrary Lagrangian-Eulerian approach. NASA Glenn Research Center, 2003.

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25

Center, NASA Glenn Research, ed. Finite element simulation of a space shuttle solid rocket booster aft skirt splashdown using an arbitrary Lagrangian-Eulerian approach. NASA Glenn Research Center, 2003.

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26

Mann, Peter. Liouville’s Theorem & Classical Statistical Mechanics. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198822370.003.0020.

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This chapter returns to the discussion of constrained Hamiltonian dynamics, now in the canonical setting, including topics such as regular Lagrangians, constraint surfaces, Hessian conditions and the constrained action principle. The standard approach to Hamiltonian mechanics is to treat all the variables as being independent; in the constrained case, a constraint function links the variables so they are no longer independent. In this chapter, the Dirac–Bergmann theory for singular Lagrangians is developed, using an action-based approach. The chapter then investigates consistency conditions an

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27

Canarutto, Daniel. Gauge Field Theory in Natural Geometric Language. Oxford University Press, 2020. http://dx.doi.org/10.1093/oso/9780198861492.001.0001.

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This monograph addresses the need to clarify basic mathematical concepts at the crossroad between gravitation and quantum physics. Selected mathematical and theoretical topics are exposed within a not-too-short, integrated approach that exploits standard and non-standard notions in natural geometric language. The role of structure groups can be regarded as secondary even in the treatment of the gauge fields themselves. Two-spinors yield a partly original ‘minimal geometric data’ approach to Einstein-Cartan-Maxwell-Dirac fields. The gravitational field is jointly represented by a spinor connect

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28

Sorrentino, Alfonso. The Hamilton-Jacobi Equation and Weak KAM Theory. Princeton University Press, 2017. http://dx.doi.org/10.23943/princeton/9780691164502.003.0005.

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This chapter describes another interesting approach to the study of invariant sets provided by the so-called weak KAM theory, developed by Albert Fathi. This approach can be considered as the functional analytic counterpart of the variational methods discussed in the previous chapters. The starting point is the relation between KAM tori (or more generally, invariant Lagrangian graphs) and classical solutions and subsolutions of the Hamilton–Jacobi equation. It introduces the notion of weak (non-classical) solutions of the Hamilton–Jacobi equation and a special class of subsolutions (critical s

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29

Godfrey, L. G. Misspecification Tests in Econometrics: The Lagrange Multiplier Principle and Other Approaches (Econometric Society Monographs). Cambridge University Press, 1991.

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30

Godfrey, L. G. Misspecification Tests in Econometrics: The Lagrange Multiplier Principle and Other Approaches (Econometric Society Monographs). Cambridge University Press, 1989.

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31

Kachelriess, Michael. Thermal field theory. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198802877.003.0015.

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After a review of the calculational approaches, the free energy of scalar particles in thermal equilibrium is calculated. The IR behaviour of mass-less scalar fields is examined, finding that a resummation of IR divergent terms is necessary. In general, particles acquire a temperature-dependent (Debye) mass, while symmetries of the Lagrangian may be hidden at low temperatures. In an appendix, the basics of equilibrium statistical physics is reviewe

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32

Mann, Peter. Differential Equations. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198822370.003.0035.

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This chapter presents the general formulation of the calculus of variations as applied to mechanics, relativity and field theories. The calculus of variations is a common mathematical technique used throughout classical mechanics. First developed by Euler to determine the shortest paths between fixed points along a surface, it was applied by Lagrange to mechanical problems in analytical mechanics. The variational problems in the chapter have been simplified for ease of understanding upon first introduction, in order to give a general mathematical framework. This chapter takes a relaxed approac

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33

Kachelriess, Michael. Quantum mechanics. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198802877.003.0002.

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After a brief review of the operator approach to quantum mechanics, Feynmans path integral, which expresses a transition amplitude as a sum over all paths, is derived. Adding a linear coupling to an external source J and a damping term to the Lagrangian, the ground-state persistence amplitude is obtained. This quantity serves as the generating functional Z[J] for n-point Green functions which are the main target when studying quantum field theory. Then the harmonic oscillator as an example for a one-dimensional quantum field theory is discussed and the reason why a relativistic quantum theory

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34

Tiwari, Sandip. Electromechanics and its devices. Oxford University Press, 2017. http://dx.doi.org/10.1093/oso/9780198759874.003.0005.

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Electromechanics—coupling of mechanical forces with others—exhibits a continuum-to-discrete spectrum of properties. In this chapter, classical and newer analysis techniques are developed for devices ranging from inertial sensors to scanning probes to quantify limits and sensitivities. Mechanical response, energy storage, transduction and dynamic characteristics of various devices are analyzed. The Lagrangian approach is developed for multidomain analysis and to bring out nonlinearity. The approach is extended to nanoscale fluidic systems where nonlinearities, fluctuation effects and the classi

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35

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

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36

Deruelle, Nathalie, and Jean-Philippe Uzan. Interacting charges II. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198786399.003.0039.

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This chapter continues the discussion from the previous chapter. The motion of a charge (m,q) in the field of another charge (m′,q′) and in its own field can now be studied in the lowest orders of the velocities directly using the equation of motion obtained in the preceding chapter. However, the features of this motion are revealed more easily by deriving them from the Darwin Lagrangian. This allows for a rigorous establishment of a balance between the energy radiated by the system and the mechanical energy lost by the system. The chapter concludes this general study of the electromagnetic ra

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37

Mann, Peter. The Hamiltonian & Phase Space. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198822370.003.0014.

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This chapter discusses the Hamiltonian and phase space. Hamilton’s equations can be derived in several ways; this chapter follows two pathways to arrive at the same result, thus giving insight into the motivation for forming these equations. The importance of deriving the same result in several ways is that it shows that, in physics, there are often several mathematical avenues to go down and that approaching a problem with, say, the calculus of variations can be entirely as valid as using a differential equation approach. The chapter extends the arenas of classical mechanics to include the co

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38

Nolte, David D. On the Shoulders of Giants. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198805847.003.0004.

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Galileo’s parabolic trajectory launched a new approach to physics that was taken up by a new generation of scientists like Isaac Newton, Robert Hooke and Edmund Halley. The English Newtonian tradition was adopted by ambitious French iconoclasts who championed Newton over their own Descartes. Chief among these was Pierre Maupertuis, whose principle of least action was developed by Leonhard Euler and Joseph Lagrange into a rigorous new science of dynamics. Along the way, Maupertuis became embroiled in a famous dispute that entangled the King of Prussia as well as the volatile Voltaire who was mo

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39

Mann, Peter. Virtual Work & d’Alembert’s Principle. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198822370.003.0013.

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This chapter discusses virtual work, returning to the Newtonian framework to derive the central Lagrange equation, using d’Alembert’s principle. It starts off with a discussion of generalised force, applied force and constraint force. Holonomic constraints and non-holonomic constraint equations are then investigated. The corresponding principles of Gauss (Gauss’s least constraint) and Jourdain are also documented and compared to d’Alembert’s approach before being generalised into the Mangeron–Deleanu principle. Kane’s equations are derived from Jourdain’s principle. The chapter closes with a d

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