Table of contents

  1. Front Matter
    Pages 1-10
  2. Linear theory

    1. Front Matter
      Pages 1-1
    2. Khanh Chau Le, Lu Trong Khiem Nguyen
      Pages 3-44
    3. Khanh Chau Le, Lu Trong Khiem Nguyen
      Pages 45-98
    4. Khanh Chau Le, Lu Trong Khiem Nguyen
      Pages 99-150
    5. Khanh Chau Le, Lu Trong Khiem Nguyen
      Pages 151-203
  3. Nonlinear theory

    1. Front Matter
      Pages 205-205
    2. Khanh Chau Le, Lu Trong Khiem Nguyen
      Pages 207-254
    3. Khanh Chau Le, Lu Trong Khiem Nguyen
      Pages 255-296
    4. Khanh Chau Le, Lu Trong Khiem Nguyen
      Pages 297-342
    5. Khanh Chau Le, Lu Trong Khiem Nguyen
      Pages 343-402
  4. Back Matter
    Pages 403-411

About this book

Introduction

Energy Methods in Dynamics is a textbook based on the lectures given by the first author at Ruhr University Bochum, Germany. Its aim is to help students acquire both a good grasp of the first principles from which the governing equations can be derived, and the adequate mathematical methods for their solving. Its distinctive features, as seen from the title, lie in the systematic and intensive use of Hamilton's variational principle and its generalizations for deriving the governing equations of conservative and dissipative mechanical systems, and also in providing the direct variational-asymptotic analysis, whenever available, of the energy and dissipation for the solution of these equations. It demonstrates that many well-known methods in dynamics like those of Lindstedt-Poincare, Bogoliubov-Mitropolsky, Kolmogorov-Arnold-Moser (KAM), Wentzel–Kramers–Brillouin (WKB),  and Whitham are derivable from this variational-asymptotic analysis.

 

This second edition includes the solutions to all exercises as well as some new materials concerning amplitude and slope modulations of nonlinear dispersive waves.

Keywords

Dissipation Energy Hamilton’s Variational Principle and its Generalization Variational-asymptotic Method

Authors and affiliations

  • Khanh Chau Le
    • 1
  • Lu Trong Khiem Nguyen
    • 2
  1. 1.Lehrstuhl für Mechanik und Material TheorieRuhr Universität BochumBochumGermany
  2. 2.Lehrstuhl für Mechanik und Material TheorieRuhr Universität BochumBochumGermany

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-05419-3
  • Copyright Information Springer International Publishing Switzerland 2014
  • Publisher Name Springer, Cham
  • eBook Packages Engineering
  • Print ISBN 978-3-319-05418-6
  • Online ISBN 978-3-319-05419-3
  • Series Print ISSN 1860-6245
  • Series Online ISSN 1860-6253
  • About this book
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