The Variational Principles Of Mechanics
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The Variational Principles Of Mechanics
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Author : Cornelius Lanczos
language : en
Publisher: Courier Corporation
Release Date : 1986-01-01
The Variational Principles Of Mechanics written by Cornelius Lanczos and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 1986-01-01 with Science categories.
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.
The Variational Principles Of Mechanics
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Author : Cornelius Lanczos
language : en
Publisher:
Release Date : 1970
The Variational Principles Of Mechanics written by Cornelius Lanczos and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1970 with Dynamics categories.
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.
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 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 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.
An Introduction To Modern Variational Techniques In Mechanics And Engineering
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Author : Bozidar D. Vujanovic
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
An Introduction To Modern Variational Techniques In Mechanics And Engineering written by Bozidar D. Vujanovic 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 2012-12-06 with Technology & Engineering categories.
This book is devoted to the basic variational principles of mechanics: the Lagrange-D'Alembert differential variational principle and the Hamilton integral variational principle. These two variational principles form the main subject of contemporary analytical mechanics, and from them the whole colossal corpus of classical dynamics can be deductively derived as a part of physical theory. In recent years students and researchers of engineering and physics have begun to realize the utility of variational principles and the vast possi bilities that they offer, and have applied them as a powerful tool for the study of linear and nonlinear problems in conservative and nonconservative dynamical systems. The present book has evolved from a series of lectures to graduate stu dents and researchers in engineering given by the authors at the Depart ment of Mechanics at the University of Novi Sad Serbia, and numerous foreign universities. The objective of the authors has been to acquaint the reader with the wide possibilities to apply variational principles in numerous problems of contemporary analytical mechanics, for example, the Noether theory for finding conservation laws of conservative and nonconservative dynamical systems, application of the Hamilton-Jacobi method and the field method suitable for nonconservative dynamical systems,the variational approach to the modern optimal control theory, the application of variational methods to stability and determining the optimal shape in the elastic rod theory, among others.
Variational And Quasi Variational Inequalities In Mechanics
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Author : Alexander S. Kravchuk
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-09-04
Variational And Quasi Variational Inequalities In Mechanics written by Alexander S. Kravchuk 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 2007-09-04 with Technology & Engineering categories.
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 Models And Methods In Solid And Fluid Mechanics
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Author : Francesco dell'Isola
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-01-15
Variational Models And Methods In Solid And Fluid Mechanics written by Francesco dell'Isola 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 2012-01-15 with Technology & Engineering categories.
F. dell'Isola, L. Placidi: Variational principles are a powerful tool also for formulating field theories. - F. dell'Isola, P. Seppecher, A. Madeo: Beyond Euler-Cauchy Continua. The structure of contact actions in N-th gradient generalized continua: a generalization of the Cauchy tetrahedron argument. - B. Bourdin, G.A. Francfort: Fracture. - S. Gavrilyuk: Multiphase flow modeling via Hamilton's principle. - V. L. Berdichevsky: Introduction to stochastic variational problems. - A. Carcaterra: New concepts in damping generation and control: theoretical formulation and industrial applications. - F. dell'Isola, P. Seppecher, A. Madeo: Fluid shock wave generation at solid-material discontinuity surfaces in porous media. Variational methods give an efficient and elegant way to formulate and solve mathematical problems that are of interest to scientists and engineers. In this book three fundamental aspects of the variational formulation of mechanics will be presented: physical, mathematical and applicative ones. The first aspect concerns the investigation of the nature of real physical problems with the aim of finding the best variational formulation suitable to those problems. The second aspect is the study of the well-posedeness of those mathematical problems which need to be solved in order to draw previsions from the formulated models. And the third aspect is related to the direct application of variational analysis to solve real engineering problems.