Titlebook: Variational Principles of Continuum Mechanics; I. Fundamentals Victor Berdichevsky Book 2009 The Editor(s) (if applicable) and The Author(s

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Variational Principlespts to explain the world by means of the smallest possible number of universal laws and general principles. The most successful and fruitful attempts stem from the idea that the observable events are extreme in their character and that the general principles sought are variational, i.e. they assert

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cognizant

Continuum Mechanicsne-to-one correspondence with a set of points of some region . in three-dimensional space ... Each particle can be assigned its “name”: the coordinates of its counterpart in region .. We denote these coordinates by capital Latin letters .., .., .., in contrast to the coordinates of the observer’s fr

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Arboreal

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Ideal Compressible Fluide variational principles formulated for elastic bodies are valid for compressible fluids as well. However, they deserve special consideration because, due to a simplified energy structure, they are enriched by new interesting features.

prodrome

Steady Motion of Ideal Fluid and Elastic Body particles. If this region does not move in the observer’s frame and its boundaries are penetrable to the media (i.e. some particles leave the region while other particles enter it), then the variational principles considered are not true. However, one may expect that the same functionals, perhaps,

排斥

Principle of Least Dissipationing equations do not have a variational structure, they possess a quasi-variational structure (see Sect. 2.6). In the another extreme case, when the dissipation plays the key role while the inertia and the internal energy effects are negligible, the variational structure of the governing equations a

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Book 2009uss 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 mathematic

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