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An Introduction to Modern Variational Techniques in Mechanics and Engineering

  • Textbook
  • © 2004

Overview

Authors:
  1. B. D. Vujanovic

    1. Faculty of Technical Sciences, University of Novi Sad, Novi Sad, Serbia and Montenegro

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  2. T. M. Atanackovic

    1. Faculty of Technical Sciences, University of Novi Sad, Novi Sad, Serbia and Montenegro

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    You can also search for this author in PubMed   Google Scholar

  • Many examples and novel applications throughout
  • Competitive literature - Meirovich, Goldstein - is outdated and does not include the synthesis of topics presented here
  • Will serve a broad audience in analytical mechanics, applied variational calculus, optimal control, physics, and mechanical and aerospace engineering

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Table of contents (8 chapters)

  1. Front Matter

    Pages i-xi
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  3. The Hamiltonian Integral Variational Principle

    1. Front Matter

      Pages 195-195
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    2. The Hamiltonian Variational Principle and Its Applications

      • B. D. Vujanovic, T. M. Atanackovic
      Pages 197-213

    3. Variable End Points, Natural Boundary Conditions, Bolza Problems

      • B. D. Vujanovic, T. M. Atanackovic
      Pages 215-240

    4. Constrained Problems

      • B. D. Vujanovic, T. M. Atanackovic
      Pages 241-262

    5. Variational Principles for Elastic Rods and Columns

      • B. D. Vujanovic, T. M. Atanackovic
      Pages 263-331

  4. Back Matter

    Pages 333-346
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Keywords

About this book

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.

Reviews

"[The book has] many examples and applications throughout the chapters.... It is intended to be only a suggestive exposition for graduate and senior undergraduate students in engineering, applied mathematics and physics.... The book should be useful for students in these quoted areas and those people with some knowledge in single-integral variational problems." —Mathematical Reviews

"Variational principles have great utility in solving problems in analytical mechanics. During recent years attention has been drawn to the wide area of possibilities they offer and variational techniques are applied as important tools for studying linear and nonlinear problems in conservative and nonconservative dynamical systems. This book discusses the basic variational principles of contemporary analytical mechanics, presents a wide range of possibilities for applying them, and solves numerous concrete examples.… The book is suitable for self-study, for graduate students in applied mathematics, physics, engineering, it can be used as a text in graduate and senior undergraduate courses, and researchers also can have a practical usage of it." —Bulletin of Belgian Mathematical Society

 

Authors and Affiliations

  • Faculty of Technical Sciences, University of Novi Sad, Novi Sad, Serbia and Montenegro

    B. D. Vujanovic, T. M. Atanackovic

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