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Interaction of Mechanics and Mathematics

Variational Principles of Continuum Mechanics

I. Fundamentals

Authors: Berdichevsky, Victor

  • Concise and understandable book about variational principles of continuum mechanics
  • Accessible to applied mathematicians, physicists and engineers who have an interest in continuum mechanics
  • Interesting and innovative textbook for graduate students
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eBook 103,52 €
price for Spain (gross)
  • ISBN 978-3-540-88467-5
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover 126,35 €
price for Spain (gross)
  • ISBN 978-3-540-88466-8
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
  • The final prices may differ from the prices shown due to specifics of VAT rules
About this book

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.

Reviews

From the reviews:

“This new book goes far beyond anything currently available concerning variational principles in continuum mechanics. … We have at hand a monument that all students and professionals in applied mathematics physics and engineering will praise and naturally keep handy on their bookshelf. Teachers will find in the book a wealth of pedagogical material for many one semester courses. They and their students will appreciate the clarity simplicity and ingenuity of many arguments offered without pedantry and sacrifice of rigour.” (Gerard A. Maugin, Mathematical Reviews, Issue 2011 a)

Table of contents (13 chapters)

  • Variational Principles

    Berdichevsky, V.L.

    Pages 3-44

    Preview Buy Chapter 30,19 €
  • Thermodynamics

    Berdichevsky, V.L.

    Pages 45-65

    Preview Buy Chapter 30,19 €
  • Continuum Mechanics

    Berdichevsky, V.L.

    Pages 67-115

    Preview Buy Chapter 30,19 €
  • Principle of Least Action in Continuum Mechanics

    Berdichevsky, V.L.

    Pages 117-147

    Preview Buy Chapter 30,19 €
  • Direct Methods of Calculus of Variations

    Berdichevsky, V.L.

    Pages 149-282

    Preview Buy Chapter 30,19 €

Buy this book

eBook 103,52 €
price for Spain (gross)
  • ISBN 978-3-540-88467-5
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover 126,35 €
price for Spain (gross)
  • ISBN 978-3-540-88466-8
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
  • The final prices may differ from the prices shown due to specifics of VAT rules
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Bibliographic Information

Bibliographic Information
Book Title
Variational Principles of Continuum Mechanics
Book Subtitle
I. Fundamentals
Authors
Series Title
Interaction of Mechanics and Mathematics
Copyright
2009
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-540-88467-5
DOI
10.1007/978-3-540-88467-5
Softcover ISBN
978-3-540-88466-8
Series ISSN
1860-6245
Edition Number
1
Number of Pages
XVIII, 586
Topics