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Titlebook: Introduction to Mechanics and Symmetry; A Basic Exposition o Jerrold E. Marsden,Tudor S. Ratiu Textbook 1999Latest edition Springer Science

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书目名称Introduction to Mechanics and Symmetry
副标题A Basic Exposition o
编辑Jerrold E. Marsden,Tudor S. Ratiu
视频video
丛书名称Texts in Applied Mathematics
图书封面Titlebook: Introduction to Mechanics and Symmetry; A Basic Exposition o Jerrold E. Marsden,Tudor S. Ratiu Textbook 1999Latest edition Springer Science
描述Symmetry has always played an important role in mechanics, from fundamental formulations of basic principles to concrete applications. The theme of the book is to develop the basic theory and applications of mechanics with an emphasis on the role of symmetry. In recent times, the interest in mechanics, and in symmetry techniques in particular, has accelerated because of developments in dynamical systems, the use of geometric methods and new applications to integrable and chaotic systems, control systems, stability and bifurcation, and the study of specific rigid, fluid, plasma and elastic systems. Introduction to Mechanics and Symmetry lays the basic foundation for these topics and includes numerous specific applications, making it beneficial to physicists and engineers. This text has specific examples and applications showing how the theory works, and up-to-date techniques, all of which makes it accessible to a wide variety of readers, expecially senior undergraduate and graduate students in mathematics, physics and engineering. For this second edition, the text has been rewritten and updated for clarity throughout, with a major revamping and expansion of the exercises. Internet s
出版日期Textbook 1999Latest edition
关键词Lagrangian mechanics; Rigid body; bifurcation; dynamical systems; lie group; manifold; mathematics; mechani
版次2
doihttps://doi.org/10.1007/978-0-387-21792-5
isbn_softcover978-1-4419-3143-6
isbn_ebook978-0-387-21792-5Series ISSN 0939-2475 Series E-ISSN 2196-9949
issn_series 0939-2475
copyrightSpringer Science+Business Media New York 1999
The information of publication is updating

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Poisson Manifolds,the more general concept of a . On the other hand, we do want to understand how this bracket . associated with a symplectic structure on coadjoint orbits and with the canonical symplectic structure on .* ..These facts are developed in Chapters 13 and 14. Chapter 15 shows how this works in detail for the rigid body.
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Momentum Maps,ation of a concept that simply describes the well-known Noether theorem. Rather, it is a rich concept that is ubiquitous in the modern developments of geometric mechanics. It has led to surprising insights into many areas of mechanics and geometry.
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Computation and Properties of Momentum Maps,ft. These transformations are called .. As we shall see, in this case there is an explicit formula for the momentum map, and it is always equivariant. Many of the momentum maps one meets in practical examples are of this sort.
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Coadjoint Orbits,work of Lie, Borel, and Weil. (See Kirillov [1962, 1976b], Arnold [1966a], Kostant [1970], and Souriau [1970].) Here we give a direct proof. Alternatively, one can give a proof using general reduction theory, as in Marsden and Weinstein [1974] and Abraham and Marsden [1978].
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