Variational Principles of Continuum Mechanics (Paperback)

Victor Berdichevsky

ISBN 10: 3540884661 / ISBN 13: 9783540884668

Published by Springer-Verlag Berlin and Heidelberg GmbH & Co. KG, Berlin, 2009

About this Item

Paperback. Thereareabout500booksonvariationalprinciples. Theyareconcernedmostlywith the mathematical aspects of the topic. The major goal of this book is to discuss the physical origin of the variational principles and the intrinsic interrelations between them. For example, the Gibbs principles appear not as the rst principles of the theory of thermodynamic equilibrium but as a consequence of the Einstein formula for thermodynamic uctuations. The mathematical issues are considered as long as they shed light on the physical outcomes and/or provide a useful technique for direct study of variational problems. ThebookisacompletelyrewrittenversionoftheauthorsmonographVariational Principles of Continuum Mechanics which appeared in Russian in 1983. I have been postponing the English translation because I wished to include the variational pr- ciples of irreversible processes in the new edition. Reaching an understanding of this subject took longer than I expected. In its nal form, this book covers all aspects of the story. The part concerned with irreversible processes is tiny, but it determines the accents put on all the results presented. The other new issues included in the book are: entropy of microstructure, variational principles of vortex line dynamics, va- ational principles and integration in functional spaces, some stochastic variational problems, variational principle for probability densities of local elds in composites with random structure, variational theory of turbulence; these topics have not been covered previously in monographic literature. This is a concise and understandable book about variational principles of continuum mechanics. The book is accessible to applied mathematicians, physicists and engineers who have an interest in continuum mechanics. Shipping may be from multiple locations in the US or from the UK, depending on stock availability.

Seller Inventory # 9783540884668

Bibliographic Details

• Title: Variational Principles of Continuum Mechanics (Paperback)
• Publisher: Springer-Verlag Berlin and Heidelberg GmbH & Co. KG, Berlin
• Publication Date: 2009
• Language: English
• ISBN 10: 3540884661
• ISBN 13: 9783540884668
• Binding: Paperback
• Condition: new

About this title

Synopsis

This is a concise and understandable book about variational principles of continuum mechanics. The book is accessible to applied mathematicians, physicists and engineers who have an interest in continuum mechanics.

From the Back Cover

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.