Variational Principles In Physics

Author : Jean-Louis Basdevant
Publisher : Springer Science & Business Media
Page : 191 pages
File Size : 51,8 Mb
Release : 2007-03-12
Category : Science
ISBN : 9780387377483

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Variational Principles in Physics by Jean-Louis Basdevant Pdf

Variational principles have proven to be surprisingly fertile. For example, Fermat used variational methods to demonstrate that light follows the fastest route from one point to another, an idea which came to be a cornerstone of geometrical optics. This book explains variational principles and charts their use throughout modern physics. It examines the analytical mechanics of Lagrange and Hamilton, the basic tools of any physicist. The book also offers simple but rich first impressions of Einstein’s General Relativity, Feynman’s Quantum Mechanics, and more that reveal amazing interconnections between various fields of physics.

Author : Wolfgang Yourgrau,Stanley Mandelstam
Publisher : Courier Corporation
Page : 224 pages
File Size : 42,6 Mb
Release : 2012-04-26
Category : Science
ISBN : 9780486151137

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Variational Principles in Dynamics and Quantum Theory by Wolfgang Yourgrau,Stanley Mandelstam Pdf

DIVHistorical, theoretical survey with many insights, much hard-to-find material. Hamilton’s principle, Hamilton-Jacobi equation, etc. /div

Author : Douglas Cline
Publisher : Unknown
Page : 128 pages
File Size : 53,7 Mb
Release : 2018-08
Category : Electronic
ISBN : 099883727X

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Variational Principles in Classical Mechanics by Douglas Cline Pdf

Two dramatically different philosophical approaches to classical mechanics were proposed during the 17th - 18th centuries. Newton developed his vectorial formulation that uses time-dependent differential equations of motion to relate vector observables like force and rate of change of momentum. Euler, Lagrange, Hamilton, and Jacobi, developed powerful alternative variational formulations based on the assumption that nature follows the principle of least action. These variational formulations now play a pivotal role in science and engineering.This book introduces variational principles and their application to classical mechanics. The relative merits of the intuitive Newtonian vectorial formulation, and the more powerful variational formulations are compared. Applications to a wide variety of topics illustrate the intellectual beauty, remarkable power, and broad scope provided by use of variational principles in physics.The second edition adds discussion of the use of variational principles applied to the following topics:(1) Systems subject to initial boundary conditions(2) The hierarchy of related formulations based on action, Lagrangian, Hamiltonian, and equations of motion, to systems that involve symmetries.(3) Non-conservative systems.(4) Variable-mass systems.(5) The General Theory of Relativity.Douglas Cline is a Professor of Physics in the Department of Physics and Astronomy, University of Rochester, Rochester, New York.

Author : Robert K. Nesbet
Publisher : Cambridge University Press
Page : 245 pages
File Size : 42,5 Mb
Release : 2002-11-14
Category : Science
ISBN : 9781139435697

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Variational Principles and Methods in Theoretical Physics and Chemistry by Robert K. Nesbet Pdf

This book brings together the essential ideas and methods behind applications of variational theory in theoretical physics and chemistry. The emphasis is on understanding physical and computational applications of variational methodology rather than on rigorous mathematical formalism. The text begins with an historical survey of familiar variational principles in classical mechanics and optimization theory, then proceeds to develop the variational principles and formalism behind current computational methodology for bound and continuum quantum states of interacting electrons in atoms, molecules, and condensed matter. It covers multiple-scattering theory, including a detailed presentation of contemporary methodology for electron-impact rotational and vibrational excitation of molecules. The book ends with an introduction to the variational theory of relativistic fields. Ideal for graduate students and researchers in any field that uses variational methodology, this book is particularly suitable as a backup reference for lecture courses in mathematical methods in physics and theoretical chemistry.

Author : David Bleecker
Publisher : Courier Corporation
Page : 253 pages
File Size : 52,8 Mb
Release : 2013-01-18
Category : Science
ISBN : 9780486151878

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Gauge Theory and Variational Principles by David Bleecker Pdf

This text provides a framework for describing and organizing the basic forces of nature and the interactions of subatomic particles. A detailed and self-contained mathematical account of gauge theory, it is geared toward beginning graduate students and advanced undergraduates in mathematics and physics. This well-organized treatment supplements its rigor with intuitive ideas. Starting with an examination of principal fiber bundles and connections, the text explores curvature; particle fields, Lagrangians, and gauge invariance; Lagrange's equation for particle fields; and the inhomogeneous field equation. Additional topics include free Dirac electron fields; interactions; calculus on frame bundle; and unification of gauge fields and gravitation. The text concludes with references, a selected bibliography, an index of notation, and a general index.

Author : Lánczos Kornél
Publisher : Unknown
Page : 307 pages
File Size : 49,6 Mb
Release : 1952
Category : Electronic
ISBN : OCLC:909085169

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The Variational Principles of Mechanics by Lánczos Kornél Pdf

Author : B. L. Moiseiwitsch
Publisher : Courier Corporation
Page : 534 pages
File Size : 52,7 Mb
Release : 2013-02-20
Category : Mathematics
ISBN : 9780486150499

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Variational Principles by B. L. Moiseiwitsch Pdf

This graduate-level text's primary objective is to demonstrate the expression of the equations of the various branches of mathematical physics in the succinct and elegant form of variational principles (and thereby illuminate their interrelationship). Its related intentions are to show how variational principles may be employed to determine the discrete eigenvalues for stationary state problems and to illustrate how to find the values of quantities (such as the phase shifts) that arise in the theory of scattering. Chapter-by-chapter treatment consists of analytical dynamics; optics, wave mechanics, and quantum mechanics; field equations; eigenvalue problems; and scattering theory. 1966 edition. Bibliography. Index.

Author : Cornelius Lanczos
Publisher : Courier Corporation
Page : 466 pages
File Size : 49,5 Mb
Release : 1986-01-01
Category : Science
ISBN : 9780486650678

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The Variational Principles of Mechanics by Cornelius Lanczos Pdf

Philosophic, less formalistic approach to analytical mechanics offers model of clear, scholarly exposition at graduate level with coverage of basics, calculus of variations, principle of virtual work, equations of motion, more.

Author : Alexandru Kristály,V. Rădulescu,Vicenţiu D. Rădulescu,Csaba Varga
Publisher : Cambridge University Press
Page : 385 pages
File Size : 52,5 Mb
Release : 2010-08-19
Category : Mathematics
ISBN : 9780521117821

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Variational Principles in Mathematical Physics, Geometry, and Economics by Alexandru Kristály,V. Rădulescu,Vicenţiu D. Rădulescu,Csaba Varga Pdf

A comprehensive introduction to modern applied functional analysis. Assumes only basic notions of calculus, real analysis, geometry, and differential equations.

Author : Victor Berdichevsky
Publisher : Springer Science & Business Media
Page : 590 pages
File Size : 45,7 Mb
Release : 2009-09-18
Category : Science
ISBN : 9783540884675

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Variational Principles of Continuum Mechanics by Victor Berdichevsky Pdf

Thereareabout500booksonvariationalprinciples. Theyareconcernedmostlywith the mathematical aspects of the topic. The major goal of this book is to discuss the physical origin of the variational principles and the intrinsic interrelations between them. For example, the Gibbs principles appear not as the rst principles of the theory of thermodynamic equilibrium but as a consequence of the Einstein formula for thermodynamic uctuations. The mathematical issues are considered as long as they shed light on the physical outcomes and/or provide a useful technique for direct study of variational problems. Thebookisacompletelyrewrittenversionoftheauthor’smonographVariational Principles of Continuum Mechanics which appeared in Russian in 1983. I have been postponing the English translation because I wished to include the variational pr- ciples of irreversible processes in the new edition. Reaching an understanding of this subject took longer than I expected. In its nal form, this book covers all aspects of the story. The part concerned with irreversible processes is tiny, but it determines the accents put on all the results presented. The other new issues included in the book are: entropy of microstructure, variational principles of vortex line dynamics, va- ational principles and integration in functional spaces, some stochastic variational problems, variational principle for probability densities of local elds in composites with random structure, variational theory of turbulence; these topics have not been covered previously in monographic literature.

Author : Boris A Kupershmidt
Publisher : World Scientific Publishing Company
Page : 444 pages
File Size : 54,9 Mb
Release : 1992-12-31
Category : Mathematics
ISBN : 9789813103658

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The Variational Principles of Dynamics by Boris A Kupershmidt Pdf

Given a conservative dynamical system of classical physics, how does one find a variational principle for it? Is there a canonical recipe for such a principle? The case of particle mechanics was settled by Lagrange in 1788; this text treats continuous systems. Recipes devised are algebraic in nature, and this book develops all the mathematical tools found necessary after the minute examination of the adiabatic fluid dynamics in the introduction. These tools include: Lagrangian and Hamiltonian formalisms, Legendre transforms, dual spaces of Lie algebras and associated 2-cocycles; and linearized and Z2-graded versions of all of these. The following typical physical systems, together with their Hamiltonian structures, are discussed: Classical Magnetohydro-dynamics with its Hall deformation; Multifluid Plasma; Superfluid He-4 (both irrotational and rotating) and 3He-A; Quantum fluids; Yang-Mills MHD; Spinning fluids; Spin Glass; Extended YM Plasma; A Lattice Gas. Detailed motivations, easy-to-follow arguments, open problems, and over 300 exercises help the reader. Request Inspection Copy

Author : Don S. Lemons
Publisher : Princeton University Press
Page : 140 pages
File Size : 41,8 Mb
Release : 1997-03-23
Category : Mathematics
ISBN : 0691026637

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Perfect Form by Don S. Lemons Pdf

All natural curves and shapes, and many artificial ones, manifest such "perfect form" because physical principles can be expressed as a statement requiring some important physical quantity to be mathematically maximum, minimum, or stationary.

Author : David Lovelock,Hanno Rund
Publisher : Courier Corporation
Page : 400 pages
File Size : 41,8 Mb
Release : 2012-04-20
Category : Mathematics
ISBN : 9780486131986

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Tensors, Differential Forms, and Variational Principles by David Lovelock,Hanno Rund Pdf

Incisive, self-contained account of tensor analysis and the calculus of exterior differential forms, interaction between the concept of invariance and the calculus of variations. Emphasis is on analytical techniques. Includes problems.

Author : Kevin W. Cassel
Publisher : Cambridge University Press
Page : 433 pages
File Size : 47,7 Mb
Release : 2013-07-22
Category : Mathematics
ISBN : 9781107022584

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Variational Methods with Applications in Science and Engineering by Kevin W. Cassel Pdf

This book reflects the strong connection between calculus of variations and the applications for which variational methods form the foundation.

Author : P. Kramer,M. Saraceno
Publisher : Unknown
Page : 108 pages
File Size : 51,8 Mb
Release : 2014-01-15
Category : Electronic
ISBN : 3662173379

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Geometry of the Time-Dependent Variational Principle in Quantum Mechanics by P. Kramer,M. Saraceno Pdf