The Variational Principles of Dynamics (Advanced Series in Mathematical Physics) [Hardcover]

Boris A. Kupershmidt (Author)

Book Description

ISBN-10: 9810202741 | ISBN-13: 978-9810202743 | Publication Date: March 1993

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.

Editorial Reviews

Review

"This book yields a self-contained, rigorous but also very clearly written account of the subject ... the book also contains a 'wealth' of apparently carefully selected and often very amusing citations from various sources." Mathematical Reviews --This text refers to an out of print or unavailable edition of this title.

Product Details

• Hardcover: 422 pages
• Publisher: World Scientific Pub Co Inc (March 1993)
• Language: English
• ISBN-10: 9810202741
• ISBN-13: 978-9810202743
• Amazon Best Sellers Rank: #8,780,333 in Books (See Top 100 in Books)

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