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Energy Methods in Dynamics (Interaction of Mechanics and Mathematics)

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9783319054186: Energy Methods in Dynamics (Interaction of Mechanics and Mathematics)
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<P><I>ENERGY METHODS IN DYNAMICS </I>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.</P><P>THIS SECOND EDITION INCLUDES THE SOLUTIONS TO ALL EXERCISES AS WELL AS SOME NEW MATERIALS CONCERNING AMPLITUDE AND SLOPE MODULATIONS OF NONLINEAR DISPERSIVE WAVES.</P>

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“This textbook is addressed to teachers and students of mechanical and civil engineering. ... To help the reader to become more proficient, each chapter ends with exercises some of which can be solved effectively by using Mathematica. ... The main goal of this textbook is to help readers to acquire both a good grasp of the first principles from which the igoverning equations can be derived, and the adequate mathematical methods for their solving.” (Vasile Marinca, zbMATH, Vol. 1303, 2015)

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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.

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9783642224034: Energy Methods in Dynamics: 1 (Interaction of Mechanics and Mathematics)

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ISBN 10: 3642224032 ISBN 13: 9783642224034
Verlag: Springer, 2011
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Verlag: Springer International Publishing (2014)
ISBN 10: 331905418X ISBN 13: 9783319054186
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Buchbeschreibung Taschenbuch. Zustand: Neu. Druck auf Anfrage Neuware -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. 428 pp. Englisch. Artikel-Nr. 9783319054186

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