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Titlebook: Global Aspects of Classical Integrable Systems; Richard H. Cushman,Larry M. Bates Book 19971st edition Springer Basel AG 1997 algebra.clas

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發(fā)表于 2025-3-21 19:46:11 | 只看該作者 |倒序?yàn)g覽 |閱讀模式
書目名稱Global Aspects of Classical Integrable Systems
編輯Richard H. Cushman,Larry M. Bates
視頻videohttp://file.papertrans.cn/387/386027/386027.mp4
圖書封面Titlebook: Global Aspects of Classical Integrable Systems;  Richard H. Cushman,Larry M. Bates Book 19971st edition Springer Basel AG 1997 algebra.clas
描述This book gives a complete global geometric description of the motion of the two di- mensional hannonic oscillator, the Kepler problem, the Euler top, the spherical pendulum and the Lagrange top. These classical integrable Hamiltonian systems one sees treated in almost every physics book on classical mechanics. So why is this book necessary? The answer is that the standard treatments are not complete. For instance in physics books one cannot see the monodromy in the spherical pendulum from its explicit solution in terms of elliptic functions nor can one read off from the explicit solution the fact that a tennis racket makes a near half twist when it is tossed so as to spin nearly about its intermediate axis. Modem mathematics books on mechanics do not use the symplectic geometric tools they develop to treat the qualitative features of these problems either. One reason for this is that their basic tool for removing symmetries of Hamiltonian systems, called regular reduction, is not general enough to handle removal of the symmetries which occur in the spherical pendulum or in the Lagrange top. For these symmetries one needs singular reduction. Another reason is that the obstructions
出版日期Book 19971st edition
關(guān)鍵詞algebra; classical mechanics; hamiltonian mechanics; manifold; pendulum
版次1
doihttps://doi.org/10.1007/978-3-0348-8891-2
isbn_softcover978-3-0348-9817-1
isbn_ebook978-3-0348-8891-2
copyrightSpringer Basel AG 1997
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Human Rights and Free Trade in Mexicommetry which gives rise to a conserved angular momentum. Thus the spherical pendulum is a Liouville integrable Hamiltonian system. Using the technique of singular reduction (see appendix B section 5) we remove the axial symmetry to obtain a Hamiltonian systems with one degree of freedom which we ana
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Physically, the harmonic oscillator in the plane is described by a particle of unit mass acted upon by two linear springs of unit spring constant: one spring acting in the . -direction and the other in the .-direction.
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