The Variational Principles of Mechanics

Author: Cornelius Lanczos
Publisher: Courier Corporation
ISBN: 0486134709
Format: PDF, ePub, Mobi
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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.

Tensors Differential Forms and Variational Principles

Author: David Lovelock
Publisher: Courier Corporation
ISBN: 048613198X
Format: PDF, ePub, Mobi
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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.

Variational Principles of Continuum Mechanics

Author: Victor Berdichevsky
Publisher: Springer Science & Business Media
ISBN: 354088467X
Format: PDF, Mobi
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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.

A History of Mechanics

Author: René Dugas
Publisher: Courier Corporation
ISBN: 0486173372
Format: PDF, Mobi
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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.

The Principles of Statistical Mechanics

Author: Richard Chace Tolman
Publisher: Courier Corporation
ISBN: 9780486638966
Format: PDF, Docs
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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.

Gauge Theory and Variational Principles

Author: David Bleecker
Publisher: Courier Corporation
ISBN: 0486445461
Format: PDF, Mobi
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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.

Calculus of Variations

Author: I. M. Gelfand
Publisher: Courier Corporation
ISBN: 0486135012
Format: PDF
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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.

Variational Principles

Author: B. L. Moiseiwitsch
Publisher: Courier Corporation
ISBN: 0486150496
Format: PDF, ePub
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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.

Calculus of Variations

Author: Robert Weinstock
Publisher: Courier Corporation
ISBN: 9780486630694
Format: PDF, Kindle
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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.