Variational Methods In Theoretical Mechanics

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Variational Methods In Theoretical Mechanics

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Author : J.T. Oden
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Variational Methods In Theoretical Mechanics written by J.T. Oden 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 is a textbook written for use in a graduate-level course for students of mechanics and engineering science. It is designed to cover the essential features of modern variational methods and to demonstrate how a number of basic mathematical concepts can be used to produce a unified theory of variational mechanics. As prerequisite to using this text, we assume that the student is equipped with an introductory course in functional analysis at a level roughly equal to that covered, for example, in Kolmogorov and Fomin (Functional Analysis, Vol. I, Graylock, Rochester, 1957) and possibly a graduate-level course in continuum mechanics. Numerous references to supplementary material are listed throughout the book. We are indebted to Professor Jim Douglas of the University of Chicago, who read an earlier version of the manuscript and whose detailed suggestions were extremely helpful in preparing the final draft. He also gratefully acknowledge that much of our own research work on variational theory was supported by the U.S. Air Force Office of Scientific Research. He are indebted to Mr. Ming-Goei Sheu for help in proofreading. Finally, we wish to express thanks to Mrs. Marilyn Gude for her excellent and pains taking job of typing the manuscript. J. T. ODEN J. N. REDDY Table of Contents PREFACE 1. INTRODUCTION 1.1 The Role of Variational Theory in Mechanics. 1 1.2 Some Historical Comments ......... . 2 1.3 Plan of Study ............... . 5 7 2. MATHEMATICAL FOUNDATIONS OF CLASSICAL VARIATIONAL THEORY 7 2.1 Introduction . . . . . . . .

Variational Methods In Theoretical Mechanics

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Author : J. Tinsley Oden
language : en
Publisher:
Release Date : 1998

Variational Methods In Theoretical Mechanics written by J. Tinsley Oden and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998 with categories.

Variational Methods In Theoretical Mechanics

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Author : J. T. Oden
language : en
Publisher:
Release Date : 1982-11-01

Variational Methods In Theoretical Mechanics written by J. T. Oden and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1982-11-01 with categories.

Variational Methods In Theoretical Mechanics

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Author : J T Oden
language : en
Publisher:
Release Date : 1976-03-01

Variational Methods In Theoretical Mechanics written by J T Oden and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1976-03-01 with 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 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.

Mathematical Methods Of Classical Mechanics

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Author : V.I. Arnol'd
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-09

Mathematical Methods Of Classical Mechanics written by V.I. Arnol'd 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 2013-04-09 with Mathematics categories.

In this text, the author constructs the mathematical apparatus of classical mechanics from the beginning, examining all the basic problems in dynamics, including the theory of oscillations, the theory of rigid body motion, and the Hamiltonian formalism. This modern approch, based on the theory of the geometry of manifolds, distinguishes iteself from the traditional approach of standard textbooks. Geometrical considerations are emphasized throughout and include phase spaces and flows, vector fields, and Lie groups. The work includes a detailed discussion of qualitative methods of the theory of dynamical systems and of asymptotic methods like perturbation techniques, averaging, and adiabatic invariance.

Mathematical Methods In Physics

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Author : Philippe Blanchard
language : en
Publisher: Birkhäuser
Release Date : 2002-10-04

Mathematical Methods In Physics written by Philippe Blanchard and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002-10-04 with Mathematics categories.

Physics has long been regarded as a wellspring of mathematical problems. Mathematical Methods in Physics is a self-contained presentation, driven by historic motivations, excellent examples, detailed proofs, and a focus on those parts of mathematics that are needed in more ambitious courses on quantum mechanics and classical and quantum field theory. Aimed primarily at a broad community of graduate students in mathematics, mathematical physics, physics and engineering, as well as researchers in these disciplines.

Models And Analysis Of Quasistatic Contact

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Author : Meir Shillor
language : en
Publisher: Springer Science & Business Media
Release Date : 2004-09-16

Models And Analysis Of Quasistatic Contact written by Meir Shillor 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 2004-09-16 with Science categories.

The mathematical theory of contact mechanics is a growing field in engineering and scientific computing. This book is intended as a unified and readily accessible source for mathematicians, applied mathematicians, mechanicians, engineers and scientists, as well as advanced students. The first part describes models of the processes involved like friction, heat generation and thermal effects, wear, adhesion and damage. The second part presents many mathematical models of practical interest and demonstrates the close interaction and cross-fertilization between contact mechanics and the theory of variational inequalities. The last part reviews further results, gives many references to current research and discusses open problems and future developments. The book can be read by mechanical engineers interested in applications. In addition, some theorems and their proofs are given as examples for the mathematical tools used in the models.

Solid Mechanics

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Author : Clive L. Dym
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-05

Solid Mechanics written by Clive L. Dym 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 2013-04-05 with Science categories.

Solid Mechanics: A Variational Approach, Augmented Edition presents a lucid and thoroughly developed approach to solid mechanics for students engaged in the study of elastic structures not seen in other texts currently on the market. This work offers a clear and carefully prepared exposition of variational techniques as they are applied to solid mechanics. Unlike other books in this field, Dym and Shames treat all the necessary theory needed for the study of solid mechanics and include extensive applications. Of particular note is the variational approach used in developing consistent structural theories and in obtaining exact and approximate solutions for many problems. Based on both semester and year-long courses taught to undergraduate seniors and graduate students, this text is geared for programs in aeronautical, civil, and mechanical engineering, and in engineering science. The authors’ objective is two-fold: first, to introduce the student to the theory of structures (one- and two-dimensional) as developed from the three-dimensional theory of elasticity; and second, to introduce the student to the strength and utility of variational principles and methods, including briefly making the connection to finite element methods. A complete set of homework problems is included.