Energy Methods in Dynamics. 1st ed. 2012

種類:

電子ブック

責任表示:

by Khanh Chau Le

出版情報:

Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2012

著者名:

• Le, Khanh Chau.
• SpringerLink (Online service)

シリーズ名:

Interaction of Mechanics and Mathematics ;

ISBN:

9783642224041 [3642224040]    

注記:

I Linear theory -- 1 Single oscillator -- 2 Coupled oscillator -- 3 Continuous oscillator -- 4 Linear waves -- II Nonlinear theory -- 5 Single oscillator -- 6 Forced oscillator -- 7 Coupled oscillator -- 8 Nonlinear waves.
The above examples should make clear the necessity of understanding the mechanism of vibrations and waves in order to control them in an optimal way. However vibrations and waves are governed by differential equations which require, as a rule, rather complicated mathematical methods for their analysis. The aim of this textbook 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 will be demonstrated that many well-known methods in dynamics like those of Lindstedt-Poincare, Bogoliubov-Mitropolsky, Ko

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