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Titlebook: Energy Methods in Dynamics; Khanh Chau Le,Lu Trong Khiem Nguyen Book 2014Latest edition Springer International Publishing Switzerland 2014

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发表于 2025-3-21 19:15:10 | 显示全部楼层 |阅读模式
书目名称Energy Methods in Dynamics
编辑Khanh Chau Le,Lu Trong Khiem Nguyen
视频video
概述Gives insight into the mechanism of vibrations and waves in order to control them in an optimal way Introduction to the systematic and intensive use of Hamilton‘s variational principle and its general
丛书名称Interaction of Mechanics and Mathematics
图书封面Titlebook: Energy Methods in Dynamics;  Khanh Chau Le,Lu Trong Khiem Nguyen Book 2014Latest edition Springer International Publishing Switzerland 2014
描述.Energy Methods in Dynamics .is a textbook based on the lectures given by the first author at Ruhr University Bochum, Germany. Its aim is to help students acquire both a good grasp of the first principles from which the governing equations can be derived, and the adequate mathematical methods for their solving. Its distinctive features, as seen from the title, lie in the systematic and intensive use of Hamilton‘s variational principle and its generalizations for deriving the governing equations of conservative and dissipative mechanical systems, and also in providing the direct variational-asymptotic analysis, whenever available, of the energy and dissipation for the solution of these equations. It demonstrates that many well-known methods in dynamics like those of Lindstedt-Poincare, Bogoliubov-Mitropolsky, Kolmogorov-Arnold-Moser (KAM), Wentzel–Kramers–Brillouin (WKB), and Whitham are derivable from this variational-asymptotic analysis..This second edition includes the solutions to all exercises as well as some new materials concerning amplitude and slope modulations of nonlinear dispersive waves..
出版日期Book 2014Latest edition
关键词Dissipation; Energy; Hamilton’s Variational Principle and its Generalization; Variational-asymptotic Me
版次2
doihttps://doi.org/10.1007/978-3-319-05419-3
isbn_softcover978-3-319-05418-6
isbn_ebook978-3-319-05419-3Series ISSN 1860-6245 Series E-ISSN 1860-6253
issn_series 1860-6245
copyrightSpringer International Publishing Switzerland 2014
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发表于 2025-3-21 21:42:26 | 显示全部楼层
1860-6245 tions to all exercises as well as some new materials concerning amplitude and slope modulations of nonlinear dispersive waves..978-3-319-05418-6978-3-319-05419-3Series ISSN 1860-6245 Series E-ISSN 1860-6253
发表于 2025-3-22 02:10:08 | 显示全部楼层
Continuous Oscillatorsear chain of oscillators and then moves to the continuum models of strings, beams, membranes, and plates. The last Section is devoted to the most general continuous oscillators. The vibrations of these oscillators can be found in form of the linear superposition of the standing waves leading to the
发表于 2025-3-22 08:36:26 | 显示全部楼层
Autonomous Single Oscillator strongly on the type of the system. The solution methods may range from phase portrait and Lindstedt-Poincar’e method for conservative systems up to Bogoliubov-Mitropolsky method for systems with weak dissipation.
发表于 2025-3-22 09:57:10 | 显示全部楼层
Non-autonomous Single Oscillatorither some time-dependent parameter or a harmonic excitation. The variationalasymptotic analysis, combined with multi-scaling, belongs again to the arsenal of mostly used analytical methods of solution of variational problems containing small parameters.
发表于 2025-3-22 16:50:15 | 显示全部楼层
Coupled Oscillatorsre not integrable and can be solved only by numerical integration. The numerical solutions have to be visualized by the Poincar’e map. For mechanical systems with weak coupling the variational-asymptotic method is applicable. This enables one to study, among others, the bifurcation of nonlinear norm
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发表于 2025-3-22 23:02:45 | 显示全部楼层
1860-6245 sive use of Hamilton‘s variational principle and its general.Energy Methods in Dynamics .is a textbook based on the lectures given by the first author at Ruhr University Bochum, Germany. Its aim is to help students acquire both a good grasp of the first principles from which the governing equations
发表于 2025-3-23 01:41:20 | 显示全部楼层
,Geschlecht – Konkurrenz – Androzentrismus,ral continuous oscillators. The vibrations of these oscillators can be found in form of the linear superposition of the standing waves leading to the eigenvalue problems in infinite dimensional spaces.
发表于 2025-3-23 07:26:31 | 显示全部楼层
Gruppen, Teams und Spitzenteams,systems with weak coupling the variational-asymptotic method is applicable. This enables one to study, among others, the bifurcation of nonlinear normalmodes, KAM-theory for coupled conservative oscillators, and synchronization of the coupled self-excited oscillators.
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