Variational Principles of Continuum Mechanics

I. Fundamentals

  • Victor Berdichevsky

Part of the Interaction of Mechanics and Mathematics book series (IMM)

Table of contents

  1. Front Matter
    Pages i-xiv
  2. Fundamentals

    1. Front Matter
      Pages 1-1
    2. V.L. Berdichevsky
      Pages 3-44
    3. V.L. Berdichevsky
      Pages 45-65
    4. V.L. Berdichevsky
      Pages 67-115
    5. V.L. Berdichevsky
      Pages 117-147
    6. V.L. Berdichevsky
      Pages 149-282
  3. Variational Features of Classical Continuum Models

    1. Front Matter
      Pages 283-283
    2. V.L. Berdichevsky
      Pages 285-339
    3. V.L. Berdichevsky
      Pages 341-374
    4. V.L. Berdichevsky
      Pages 375-387
    5. V.L. Berdichevsky
      Pages 389-454
    6. V.L. Berdichevsky
      Pages 455-472
    7. V.L. Berdichevsky
      Pages 473-494
    8. V.L. Berdichevsky
      Pages 495-508
    9. V.L. Berdichevsky
      Pages 509-529
  4. Back Matter
    Pages 1-53

About this book

Introduction

The book reviews the two features of the variational approach: its use as a universal tool to describe physical phenomena and as a source for qualitative and quantitative methods of studying particular problems.

Berdichevsky’s work differs from other books on the subject in focusing mostly on the physical origin of variational principles as well as establishing their interrelations. For example, the Gibbs principles appear as a consequence of the Einstein formula for thermodynamic fluctuations rather than as the first principles of the theory of thermodynamic equilibrium. Mathematical issues are considered as long as they shed light on the physical outcomes and/or provide a useful technique for the direct study of variational problems. In addition, a thorough account of variational principles discovered in various branches of continuum mechanics is given.

In this book, the first volume, the author covers the variational principles for systems with a finite number of degrees of freedom; the variational principles of thermodynamics; the basics of continuum mechanics; the variational principles for classical models of continuum mechanics, such as elastic and plastic bodies, and ideal and viscous fluids; and direct methods of calculus of variations.

Keywords

Calculus of Variations Degrees of freedom Dissipation Entropy Variational Principles calculus continuum mechanics mechanics statics thermodynamics

Authors and affiliations

  • Victor Berdichevsky
    • 1
  1. 1.Mechanical Engineering Dept.Wayne State UniversityDetroitU.S.A.

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-540-88467-5
  • Copyright Information Springer-Verlag Berlin Heidelberg 2009
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Engineering
  • Print ISBN 978-3-540-88466-8
  • Online ISBN 978-3-540-88467-5
  • Series Print ISSN 1860-6245
  • Series Online ISSN 1860-6253
  • About this book