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# 📙 Variational Principles of Continuum Mechanics: I. Fundamentals by Victor Berdichevsky (auth.) — free epub

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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.

- Series:
**Interaction of Mechanics and Mathematics** - Author:
**Victor Berdichevsky (auth.)** - Year:
**2009** - Publisher:
**Springer-Verlag Berlin Heidelberg** - Language:
**English** - ISBN:
**3540884661,9783540884668**

- File size:
**3 430 100** - Format:
**pdf**

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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...

This book is the first to present an overview of higher-order Hamilton geometry with applications to higher-order Hamiltonian mechanics. It is a direct continuation of the book The Geometry of Hamilton and Lagrange Spaces, (Kluwer Academic Publishers, ...

This book focuses on the fundamental ideas of continuum mechanics by analyzing models of fluid flow and solid deformation and examining problems in elasticity, water waves, and extremum principles. Mathematics Applied to Continuum Mechanics gives an overv...

The book provides a rigorous axiomatic approach to continuum mechanics under large deformation. In addition to the classical nonlinear continuum mechanics – kinematics, fundamental laws, the theory of functions having jump discontinuities across singular ...

Devoted to the classical continuum theory of solids and fluids as well as selected topics of modern continuum mechanics of viscoelasticity and microcontinua together with their applications to problems of practical interest. Highlights the derivation of c...

The book provides a rigorous axiomatic approach to continuum mechanics under large deformation. In addition to the classical nonlinear continuum mechanics – kinematics, fundamental laws, the theory of functions having jump discontinuities across singular ...

This concise textbook develops step by step the fundamental principles of continuum mechanics. Emphasis is on mathematical clarity, and an extended appendix provides the required background knowledge in linear algebra and tensor calculus. After introducin...

Fundamentals of Continuum Mechanics of Soils provides a long-needed general scheme for the study of the important yet problematic material of soil. It closes the gap between two disciplines, soil mechanics and con- tinuum mechanics, showing that the famil...

The books Fractional Calculus with Applications in Mechanics: Vibrations and Diffusion Processes and Fractional Calculus with Applications in Mechanics: Wave Propagation, Impact and Variational Principles contain various applications of fractional calculu...

This book is an up-to-date, comprehensive review of the neuropsychiatry of different types of cognitive impairment by active authorities in the field. There is an emphasis on diagnostic and management issues. Cognitive impairment both with and without cri...

This book reconstructs the lines of nihilism that Walter Benjamin took from Friedrich Nietzsche that define both his theory of art and the avant-garde, and his approach to political action. It retraces the eccentric route of Benjamin's philosophical disco...

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This book presents an authoritative overview of the emerging field of person-centered psychiatry. This perspective, articulating science and humanism, arose within the World Psychiatric Association and aims to shift the focus of psychiatry from organ and ...

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This volume explores the work environment in multinational corporations. To do so, it integrates studies on the organizational sciences, cross-cultural management, positive psychology and sociology within a single comprehensive framework. Twenty-two autho...

In this study Arun Bala examines the implications that Niels Bohr’s principle of complementarity holds for fields beyond physics. Bohr, one of the founding figures of modern quantum physics, argued that the principle of complementarity he proposed for und...