The Variational Principles Of Dynamics

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Variational Principles In Dynamics And Quantum Theory

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Author : Wolfgang Yourgrau
language : en
Publisher: Courier Corporation
Release Date : 2012-04-26

Variational Principles In Dynamics And Quantum Theory written by Wolfgang Yourgrau and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-04-26 with Science categories.

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

The Variational Principles Of Dynamics

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Author : Boris A Kuperschmidt
language : en
Publisher: World Scientific Publishing Company
Release Date : 1992-12-31

The Variational Principles Of Dynamics written by Boris A Kuperschmidt and has been published by World Scientific Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992-12-31 with Mathematics categories.

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.

Variational Principles Of Continuum Mechanics

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Author : Victor Berdichevsky
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-09-18

Variational Principles Of Continuum Mechanics written by Victor Berdichevsky and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-09-18 with Science categories.

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.

Variational Principles In Physics

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Author : Jean-Louis Basdevant
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-12-18

Variational Principles In Physics written by Jean-Louis Basdevant and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-12-18 with Science categories.

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.

Variational Principles In Classical Mechanics

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Author : Douglas Cline
language : en
Publisher:
Release Date : 2018-08

Variational Principles In Classical Mechanics written by Douglas Cline and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-08 with categories.

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.

The Variational Principles Of Dynamics

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Author : Boris A. Kupershmidt
language : en
Publisher: World Scientific Publishing Company Incorporated
Release Date : 1992-12-01

The Variational Principles Of Dynamics written by Boris A. Kupershmidt and has been published by World Scientific Publishing Company Incorporated this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992-12-01 with Mathematics categories.

The Variational Principles Of Dynamics

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Author : Boris A. Kupershmidt
language : en
Publisher:
Release Date : 1998

The Variational Principles Of Dynamics written by Boris A. Kupershmidt and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998 with categories.

The Principle Of Least Action In Geometry And Dynamics

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Author : Karl Friedrich Siburg
language : en
Publisher: Springer
Release Date : 2004-04-30

The Principle Of Least Action In Geometry And Dynamics written by Karl Friedrich Siburg and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-04-30 with Mathematics categories.

New variational methods by Aubry, Mather, and Mane, discovered in the last twenty years, gave deep insight into the dynamics of convex Lagrangian systems. This book shows how this Principle of Least Action appears in a variety of settings (billiards, length spectrum, Hofer geometry, modern symplectic geometry). Thus, topics from modern dynamical systems and modern symplectic geometry are linked in a new and sometimes surprising way. The central object is Mather’s minimal action functional. The level is for graduate students onwards, but also for researchers in any of the subjects touched in the book.

The Method Of Weighted Residuals And Variational Principles

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Author : Bruce A. Finlayson
language : en
Publisher: SIAM
Release Date : 2013-12-30

The Method Of Weighted Residuals And Variational Principles written by Bruce A. Finlayson and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-12-30 with Mathematics categories.

This classic book covers the solution of differential equations in science and engineering in such as way as to provide an introduction for novices before progressing toward increasingly more difficult problems. The Method of Weighted Residuals and Variational Principles describes variational principles, including how to find them and how to use them to construct error bounds and create stationary principles. The book also illustrates how to use simple methods to find approximate solutions, shows how to use the finite element method for more complex problems, and provides detailed information on error bounds. Problem sets make this book ideal for self-study or as a course text.

Global Formulations Of Lagrangian And Hamiltonian Dynamics On Manifolds

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Author : Taeyoung Lee
language : en
Publisher: Springer
Release Date : 2017-08-14

Global Formulations Of Lagrangian And Hamiltonian Dynamics On Manifolds written by Taeyoung Lee and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-08-14 with Mathematics categories.

This book provides an accessible introduction to the variational formulation of Lagrangian and Hamiltonian mechanics, with a novel emphasis on global descriptions of the dynamics, which is a significant conceptual departure from more traditional approaches based on the use of local coordinates on the configuration manifold. In particular, we introduce a general methodology for obtaining globally valid equations of motion on configuration manifolds that are Lie groups, homogeneous spaces, and embedded manifolds, thereby avoiding the difficulties associated with coordinate singularities. The material is presented in an approachable fashion by considering concrete configuration manifolds of increasing complexity, which then motivates and naturally leads to the more general formulation that follows. Understanding of the material is enhanced by numerous in-depth examples throughout the book, culminating in non-trivial applications involving multi-body systems. This book is written for a general audience of mathematicians, engineers, and physicists with a basic knowledge of mechanics. Some basic background in differential geometry is helpful, but not essential, as the relevant concepts are introduced in the book, thereby making the material accessible to a broad audience, and suitable for either self-study or as the basis for a graduate course in applied mathematics, engineering, or physics.