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Titlebook: Global Aspects of Classical Integrable Systems; Richard H. Cushman,Larry M. Bates Book 2015Latest edition Springer Basel 2015 algebra.clas

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書目名稱Global Aspects of Classical Integrable Systems
編輯Richard H. Cushman,Larry M. Bates
視頻videohttp://file.papertrans.cn/387/386026/386026.mp4
概述This book gives a complete global geometric description of the motion of the two dimensional harmonic oscillator, the Kepler problem, the Euler top, the spherical pendulum and the Lagrange top.This bo
圖書封面Titlebook: Global Aspects of Classical Integrable Systems;  Richard H. Cushman,Larry M. Bates Book 2015Latest edition Springer Basel 2015 algebra.clas
描述This book gives a uniquely complete description of the geometry of the energy momentum mapping of five classical integrable systems: the 2-dimensional harmonic oscillator, the geodesic flow on the 3-sphere, the Euler top, the spherical pendulum and the Lagrange top. It presents for the first time in book form a general theory of symmetry reduction which allows one to reduce the symmetries in the spherical pendulum and the Lagrange top. Also the monodromy obstruction to the existence of global action angle coordinates is calculated for the spherical pendulum and the Lagrange top. The book addresses professional mathematicians and graduate students and can be used as a textbook on advanced classical mechanics or global analysis.
出版日期Book 2015Latest edition
關鍵詞algebra; classical mechanics; hamiltonian mechanics; manifold; pendulum
版次2
doihttps://doi.org/10.1007/978-3-0348-0918-4
isbn_ebook978-3-0348-0918-4
copyrightSpringer Basel 2015
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Basic Morse Theorye the Morse isotopy lemma which gives a criterion when two suitable level sets of a smooth function are diffeomorphic. We conclude the chapter by extending the notion of nondegenerate critical point to a nondegenerate critical submanifold.
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Fundamental conceptsectic manifold, which is a Lie algebra under Poisson bracket, is made into an algebra using pointwise multiplication of smooth functions, we obtain a Poisson algebra. The symplectic formulation of mechanics can be recovered from this Poisson algebra.
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Human Resources, Employment and Developmentverns the motion of two bodies in .. under gravitational attraction. We give two methods to regularize the flow of the Kepler vector field: one energy surface by energy surface and the other for all negative energies at once.
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Context 1997–2003: History and Politicsly lifted to a horizontal curve in .. An Ehresmann connection is good if every smooth curve in . has a global horizontal lift. For good connections we define the notions of parallel translation and holonomy.
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