The Variational Principles Of Mechanics

Author: Cornelius Lanczos
Editor: Courier Corporation
ISBN: 0486134709
File Size: 29,74 MB
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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.

Examples To Extremum And Variational Principles In Mechanics

Author: Horst Lippmann
Editor: Springer
ISBN: 9783211811153
File Size: 35,50 MB
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Variational Principles In Classical Mechanics

Author: Douglas Cline
Editor:
ISBN: 9780998837277
File Size: 22,21 MB
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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.

Examples To Extremum And Variational Principles In Mechanics

Author: D. Besdo
Editor: Springer
ISBN: 3709127262
File Size: 67,11 MB
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Variational Principles Of Continuum Mechanics

Author: Victor Berdichevsky
Editor: Springer Science & Business Media
ISBN: 354088467X
File Size: 17,82 MB
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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 Dynamics And Quantum Theory

Author: Wolfgang Yourgrau
Editor: Courier Corporation
ISBN: 0486151131
File Size: 49,99 MB
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DIVHistorical, theoretical survey with many insights, much hard-to-find material. Hamilton’s principle, Hamilton-Jacobi equation, etc. /div

The Variational Principles Of Mechanics

Author: Cornelius Lanczos
Editor:
ISBN:
File Size: 38,14 MB
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The Variational Principles Of Mechanics

Author: Cornelius Lanczos
Editor:
ISBN:
File Size: 56,84 MB
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Energy Principles And Variational Methods In Applied Mechanics

Author: J. N. Reddy
Editor: John Wiley & Sons
ISBN: 9780471179856
File Size: 18,34 MB
Format: PDF
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A systematic presentation of energy principles and variationalmethods The increasing use of numerical and computational methods inengineering and applied sciences has shed new light on theimportance of energy principles and variational methods. EnergyPrinciples and Variational Methods in Applied Mechanicsprovides a systematic and practical introduction to the use ofenergy principles, traditional variational methods, and the finiteelement method to the solution of engineering problems involvingbars, beams, torsion, plane elasticity, and plates. Beginning with a review of the basic equations of mechanics andthe concepts of work, energy, and topics from variational calculus,this book presents the virtual work and energy principles, energymethods of solid and structural mechanics, Hamilton'sprinciple for dynamical systems, and classical variational methodsof approximation. A unified approach, more general than that foundin most solid mechanics books, is used to introduce the finiteelement method. Also discussed are applications to beams andplates. Complete with more than 200 illustrations and tables, EnergyPrinciples and Variational Methods in Applied Mechanics, SecondEdition is a valuable book for students of aerospace, civil,mechanical, and applied mechanics; and engineers in design andanalysis groups in the aircraft, automobile, and civil engineeringstructures, as well as shipbuilding industries.

The Variational Principles Of Mechanics

Author: Cornelius Lanczos (Physicist, Mathematician, Hungary, Germany, United States)
Editor:
ISBN:
File Size: 18,94 MB
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A Variational Principle For Compressible Fluid Mechanics

Author: Robert Joel Prozan
Editor:
ISBN:
File Size: 77,13 MB
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Inverse Variational Principles In The Fracture Mechanics And Thermodynamics Of Solids

Author: Václav Horák
Editor:
ISBN:
File Size: 31,50 MB
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Ve studii byla pravidla inverzních variačních principů, vycházejících z obvyklých variačních principů mechaniky a termodynamiky, aplikována na frakturní mechaniku a termodynamiku pevných látek. Autoru se podařilo sjednotit vucelenou logickou koncepci různé teoretické úvahy o trhlinách pevných látek. Pro ilustraci postupů jsou uvedeny dva mechanické modely trhliny pevných látek.

A Variational Principle For Compressible Fluid Mechanics Discussion Of The One Dimensional Theory

Author: Robert Joel Prozan
Editor:
ISBN:
File Size: 59,73 MB
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Variational Principles In Physics

Author: Jean-Louis Basdevant
Editor: Springer Science & Business Media
ISBN: 0387377484
File Size: 69,84 MB
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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.

Classical Mechanics With Calculus Of Variations And Optimal Control

Author: Mark Levi
Editor: American Mathematical Soc.
ISBN: 0821891383
File Size: 43,53 MB
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This is an intuitively motivated presentation of many topics in classical mechanics and related areas of control theory and calculus of variations. All topics throughout the book are treated with zero tolerance for unrevealing definitions and for proofs which leave the reader in the dark. Some areas of particular interest are: an extremely short derivation of the ellipticity of planetary orbits; a statement and an explanation of the "tennis racket paradox"; a heuristic explanation (and a rigorous treatment) of the gyroscopic effect; a revealing equivalence between the dynamics of a particle and statics of a spring; a short geometrical explanation of Pontryagin's Maximum Principle, and more. In the last chapter, aimed at more advanced readers, the Hamiltonian and the momentum are compared to forces in a certain static problem. This gives a palpable physical meaning to some seemingly abstract concepts and theorems. With minimal prerequisites consisting of basic calculus and basic undergraduate physics, this book is suitable for courses from an undergraduate to a beginning graduate level, and for a mixed audience of mathematics, physics and engineering students. Much of the enjoyment of the subject lies in solving almost 200 problems in this book.

Variational Principles And The Virial Theorem In Problems On Continuous Spectra In Quantum Mechanics

Author: Yu. N. Demkov
Editor:
ISBN:
File Size: 66,53 MB
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Variational Principles

Author: B. L. Moiseiwitsch
Editor: Courier Corporation
ISBN: 0486150496
File Size: 60,80 MB
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This text shows how variational principles are used to determine the discrete eigenvalues for stationary state problems and to illustrate how to find the values of quantities that arise in the theory of scattering. 1966 edition.

Variational And Quasi Variational Inequalities In Mechanics

Author: Alexander S. Kravchuk
Editor: Springer Science & Business Media
ISBN: 1402063776
File Size: 20,25 MB
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The essential aim of this book is to consider a wide set of problems arising in the mathematical modeling of mechanical systems under unilateral constraints. In these investigations elastic and non-elastic deformations, friction and adhesion phenomena are taken into account. All the necessary mathematical tools are given: local boundary value problem formulations, construction of variational equations and inequalities and their transition to minimization problems, existence and uniqueness theorems, and variational transformations (Friedrichs and Young-Fenchel-Moreau) to dual and saddle-point search problems.

Variational Principles And Methods In Theoretical Physics And Chemistry

Author: Robert K. Nesbet
Editor: Cambridge University Press
ISBN: 9781139435697
File Size: 30,83 MB
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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.