The Variational Principles of Mechanics

Author: Cornelius Lanczos

Publisher: Courier Corporation

ISBN: 0486134709

Category: Science

Page: 464

View: 6520

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.
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Variational Principles in Dynamics and Quantum Theory

Author: Wolfgang Yourgrau,Stanley Mandelstam

Publisher: Courier Corporation

ISBN: 0486151131

Category: Science

Page: 224

View: 8486

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

Author: René Dugas

Publisher: Courier Corporation

ISBN: 0486173372

Category: Science

Page: 688

View: 1050

Monumental study traces the history of mechanical principles chronologically from antiquity through the early 20th century. Contributions of ancient Greeks, Leonardo, Galileo, Kepler, Lagrange, others. 116 illustrations.
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The Principles of Statistical Mechanics

Author: Richard Chace Tolman

Publisher: Courier Corporation

ISBN: 9780486638966

Category: Science

Page: 660

View: 1346

This is the definitive treatise on the fundamentals of statistical mechanics. A concise exposition of classical statistical mechanics is followed by a thorough elucidation of quantum statistical mechanics: postulates, theorems, statistical ensembles, changes in quantum mechanical systems with time, and more. The final two chapters discuss applications of statistical mechanics to thermodynamic behavior. 1930 edition.
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Variational Principles of Continuum Mechanics

I. Fundamentals

Author: Victor Berdichevsky

Publisher: Springer Science & Business Media

ISBN: 354088467X

Category: Technology & Engineering

Page: 586

View: 306

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.
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Tensors, Differential Forms, and Variational Principles

Author: David Lovelock,Hanno Rund

Publisher: Courier Corporation

ISBN: 048613198X

Category: Mathematics

Page: 400

View: 7085

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.
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Calculus of Variations

Author: I. M. Gelfand,S. V. Fomin

Publisher: Courier Corporation

ISBN: 0486135012

Category: Mathematics

Page: 240

View: 3011

Fresh, lively text serves as a modern introduction to the subject, with applications to the mechanics of systems with a finite number of degrees of freedom. Ideal for math and physics students.
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Principles of Electrodynamics

Author: Melvin Schwartz

Publisher: Courier Corporation

ISBN: 0486134679

Category: Science

Page: 368

View: 9470

The 1988 Nobel Prize winner establishes the subject's mathematical background, reviews the principles of electrostatics, then introduces Einstein's special theory of relativity and applies it to topics throughout the book.
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An Introduction to the Calculus of Variations

Author: Charles Fox

Publisher: Courier Corporation

ISBN: 9780486654997

Category: Mathematics

Page: 271

View: 8739

In this highly regarded text for advanced undergraduate and graduate students, the author develops the calculus of variations both for its intrinsic interest and for its powerful applications to modern mathematical physics. Topics include first and second variations of an integral, generalizations, isoperimetrical problems, least action, special relativity, elasticity, more. 1963 edition.
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Variational Principles

Author: B. L. Moiseiwitsch

Publisher: Courier Corporation

ISBN: 0486150496

Category: Mathematics

Page: 320

View: 3371

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.
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Calculus of Variations

With Applications to Physics and Engineering

Author: Robert Weinstock

Publisher: Courier Corporation

ISBN: 9780486630694

Category: Mathematics

Page: 326

View: 7873

This text is basically divided into two parts. Chapters 1–4 include background material, basic theorems and isoperimetric problems. Chapters 5–12 are devoted to applications, geometrical optics, particle dynamics, the theory of elasticity, electrostatics, quantum mechanics, and other topics. Exercises in each chapter. 1952 edition.
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Calculus of Variations

Mechanics, Control and Other Applications

Author: Charles R. MacCluer

Publisher: Courier Corporation

ISBN: 0486278301

Category: Mathematics

Page: 272

View: 6509

First truly up-to-date treatment offers a simple introduction to optimal control, linear-quadratic control design, and more. Broad perspective features numerous exercises, hints, outlines, and appendixes, including a practical discussion of MATLAB. 2005 edition.
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Calculus of Variations

Author: L. E. Elsgolc

Publisher: Elsevier

ISBN: 1483137562

Category: Mathematics

Page: 178

View: 5719

Calculus of Variations aims to provide an understanding of the basic notions and standard methods of the calculus of variations, including the direct methods of solution of the variational problems. The wide variety of applications of variational methods to different fields of mechanics and technology has made it essential for engineers to learn the fundamentals of the calculus of variations. The book begins with a discussion of the method of variation in problems with fixed boundaries. Subsequent chapters cover variational problems with movable boundaries and some other problems; sufficiency conditions for an extremum; variational problems of constrained extrema; and direct methods of solving variational problems. Each chapter is illustrated by a large number of problems some of which are taken from existing textbooks. The solutions to the problems in each chapter are provided at the end of the book.
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Applied Analysis

Author: Cornelius Lanczos

Publisher: Courier Corporation

ISBN: 0486319261

Category: Mathematics

Page: 576

View: 8137

Classic work on analysis and design of finite processes for approximating solutions of analytical problems. Features algebraic equations, matrices, harmonic analysis, quadrature methods, and much more.
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Gauge Theory and Variational Principles

Author: David Bleecker

Publisher: Courier Corporation

ISBN: 0486445461

Category: Mathematics

Page: 181

View: 1818

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.
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Introduction to Quantum Mechanics with Applications to Chemistry

Author: Linus Pauling,E. Bright Wilson

Publisher: Courier Corporation

ISBN: 0486134938

Category: Science

Page: 496

View: 8480

Classic undergraduate text explores wave functions for the hydrogen atom, perturbation theory, the Pauli exclusion principle, and the structure of simple and complex molecules. Numerous tables and figures.
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The Quantum Theory of Radiation

Author: Walter Heitler

Publisher: Courier Corporation

ISBN: 9780486645582

Category: Science

Page: 430

View: 5371

The first comprehensive treatment of quantum physics in any language, this classic introduction to the basic theory remains highly recommended and in wide use, both as a text and as a reference. A unified and accurate guide to the application of radiative processes, it explores the mathematics and physics of quantum theory. 1954 edition.
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The Lazy Universe

An Introduction to the Principle of Least Action

Author: Jennifer Coopersmith

Publisher: Oxford University Press

ISBN: 0191060720

Category: Science

Page: 272

View: 486

This is a rare book on a rare topic: it is about 'action' and the Principle of Least Action. A surprisingly well-kept secret, these ideas are at the heart of physical science and engineering. Physics is well known as being concerned with grand conservatory principles (e.g. the conservation of energy) but equally important is the optimization principle (such as getting somewhere in the shortest time or with the least resistance). The book explains: why an optimization principle underlies physics, what action is, what `the Hamiltonian' is, and how new insights into energy, space, and time arise. It assumes some background in the physical sciences, at the level of undergraduate science, but it is not a textbook. The requisite derivations and worked examples are given but may be skim-read if desired. The author draws from Cornelius Lanczos's book "The Variational Principles of Mechanics" (1949 and 1970). Lanczos was a brilliant mathematician and educator, but his book was for a postgraduate audience. The present book is no mere copy with the difficult bits left out - it is original, and a popularization. It aims to explain ideas rather than achieve technical competence, and to show how Least Action leads into the whole of physics.
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Mechanics

Author: J. P. Den Hartog

Publisher: Courier Corporation

ISBN: 0486158691

Category: Science

Page: 480

View: 9639

This classic introductory text features hundreds of applications and design problems that illuminate fundamentals of trusses, loaded beams and cables, and related areas. Includes 334 answered problems.
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