Variational Principles of Continuum Mechanics [electronic resource] :I. Fundamentals / by Victor Berdichevsky.
by Berdichevsky, Victor [author.]; SpringerLink (Online service).
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BookSeries: Interaction of Mechanics and Mathematics: Publisher: Berlin, Heidelberg : Springer Berlin Heidelberg, 2009.Description: IX, 586 pgs, 79 illus online resource.ISBN: 9783540884675.Subject(s): Engineering | Mathematics | Mechanics | Engineering mathematics | Materials | Mechanical engineering | Engineering | Continuum Mechanics and Mechanics of Materials | Appl.Mathematics/Computational Methods of Engineering | Applications of Mathematics | Mechanics | Mechanical Engineering | Fluid- and AerodynamicsDDC classification: 620.1 Online resources: Click here to access online | Item type | Current location | Call number | Status | Date due | Barcode |
|---|---|---|---|---|---|
| QA808.2 (Browse shelf) | Available | ||||
| Long Loan | MAIN LIBRARY | TA405-409.3 (Browse shelf) | Available |
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Fundamentals -- Variational Principles -- Thermodynamics -- Continuum Mechanics -- Principle of Least Action in Continuum Mechanics -- Direct Methods of Calculus of Variations -- Variational features of classical continuum models -- Statics of a Geometrically Linear Elastic Body -- Statics of a Geometrically Nonlinear Elastic Body -- Dynamics of Elastic Bodies -- Ideal Incompressible Fluid -- Ideal Compressible Fluid -- Steady Motion of Ideal Fluid and Elastic Body -- Principle of Least Dissipation -- Motion of Rigid Bodies in Fluids.
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.
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