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The Variational Principles of Mechanics
Author: Cornelius Lanczos
Publisher: Courier Corporation
Published: 1986-01-01
Total Pages: 466
ISBN-13: 0486650677
DOWNLOAD EBOOK →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.
Variational Principles in Classical Mechanics
Author: Douglas Cline
Publisher:
Published: 2018-08
Total Pages:
ISBN-13: 9780998837277
DOWNLOAD EBOOK →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.
Variational Principles of Continuum Mechanics
Author: Victor Berdichevsky
Publisher: Springer Science & Business Media
Published: 2009-09-18
Total Pages: 590
ISBN-13: 354088467X
DOWNLOAD EBOOK →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
Publisher: Courier Corporation
Published: 1979-01-01
Total Pages: 222
ISBN-13: 9780486637730
DOWNLOAD EBOOK →Historical, theoretical survey with many insights, much hard-to-find material. Covers Hamilton's principle, Hamilton-Jacobi equation, relationship to quantum theory and wave mechanics, and more.
Variational Principles in Physics
Author: Jean-Louis Basdevant
Publisher: Springer Science & Business Media
Published: 2007-03-12
Total Pages: 191
ISBN-13: 0387377484
DOWNLOAD EBOOK →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.
Gauge Theory and Variational Principles
Author: David Bleecker
Publisher: Courier Corporation
Published: 2013-01-18
Total Pages: 253
ISBN-13: 0486151875
DOWNLOAD EBOOK →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.
Variational Principles
Author: B. L. Moiseiwitsch
Publisher: Courier Corporation
Published: 2013-02-20
Total Pages: 473
ISBN-13: 0486150496
DOWNLOAD EBOOK →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.
Mathematical Methods of Classical Mechanics
Author: V.I. Arnol'd
Publisher: Springer Science & Business Media
Published: 2013-04-09
Total Pages: 530
ISBN-13: 1475720637
DOWNLOAD EBOOK →This book constructs the mathematical apparatus of classical mechanics from the beginning, examining basic problems in dynamics like the theory of oscillations and the Hamiltonian formalism. The author emphasizes geometrical considerations and includes phase spaces and flows, vector fields, and Lie groups. Discussion includes qualitative methods of the theory of dynamical systems and of asymptotic methods like averaging and adiabatic invariance.
Computational Solid Mechanics
Author: Marco L. Bittencourt
Publisher: CRC Press
Published: 2014-09-19
Total Pages: 680
ISBN-13: 1482246538
DOWNLOAD EBOOK →Presents a Systematic Approach for Modeling Mechanical Models Using Variational Formulation-Uses Real-World Examples and Applications of Mechanical ModelsUtilizing material developed in a classroom setting and tested over a 12-year period, Computational Solid Mechanics: Variational Formulation and High-Order Approximation details an approach that e
