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(By Boris A. Kupershmidt)



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Format: DJVU

Language: English

Publisher: World Scientific Pub Co Inc



Given a conservative dynamical system of classical physics, how does one find a variational principle for it? Is there a canonical recipe for such a principle? The case of particle mechanics was settled by Lagrange in 1788; this text treats continuous systems. Recipes devised are algebraic in nature, and this book develops the mathematical tools found necessary after the minute examination of the adiabatic fluid dynamics in the introduction. These tools include: Lagrangian and Hamiltonian formalisms, Legendre transforms, dual spaces of Lie algebras and associated 2-cocyles; and linearized and Z2-graded versions of all of these. The following typical physical systems, together with their Hamiltonian structures, are discussed: classical magnetohydrodynamics with its Hall deformation; multifluid plasma; superfluid He-4 (both irrotational and rotating) and 3He-A; quantum fluids; Yang-Mills MHD; spinning fluids; spin glass; extended YM plasma; a lattice gas. Detailed motivations, open problems, and over 300 exercises help the reader. --This text refers to an out of print or unavailable edition of this title.



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Variational principles of dynamics ebook
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