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Author Le, Khanh Chau, 1955-
Title Energy methods in dynamics / Khanh Chau Le, Lu Trong Khiem Nguyen.
Imprint Cham : Springer, 2014.
Edition Second edition.

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Author Le, Khanh Chau, 1955-
Series Interaction of mechanics and mathematics, 1860-6245
Interaction of mechanics and mathematics series.
Subject Dynamics -- Mathematical models.
Vibration -- Mathematical models.
Waves -- Mathematical models.
Alt Name Nguyen, Lu Trong Khiem,
Description 1 online resource (xii, 411 pages) : illustrations.
polychrome rdacc
Edition Second edition.
Bibliography Note Includes bibliographical references and index.
Summary 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), WentzelKramersBrillouin (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.
Contents Preface to the Second Edition; Preface to the First Edition; Contents; Part I; Single Oscillator; 1.1 Harmonic Oscillator; 1.2 Damped Oscillator; 1.3 Forced Oscillator; 1.4 Harmonic Excitations and Resonance; 1.5 Exercises; Coupled Oscillators; 2.1 Conservative Oscillators; 2.2 Dissipative Oscillators; 2.3 Forced Oscillators and Vibration Control; 2.4 Variational Principles; 2.5 Oscillators with; 2.6 Exercises; Continuous Oscillators; 3.1 Chain of Oscillators; 3.2 String; 3.3 Beam; 3.4 Membrane; 3.5 Plate; 3.6 General Continuous Oscillators; 3.7 Exercises; LinearWaves; 4.1 HyperbolicWaves.
4.2 DispersiveWaves4.3 ElasticWaveguide; 4.4 Energy Method; 4.5 Exercises; Part II; Autonomous Single Oscillator; 5.1 Conservative Oscillator; 5.2 Dissipative Oscillator; 5.3 Self-excited Oscillator; 5.4 Oscillator withWeak or Strong Dissipation; 5.5 Exercises; Non-autonomous Single Oscillator; 6.1 Parametrically-Excited Oscillator; 6.2 Mathieu's Differential Equation; 6.3 Duffing's Forced Oscillator; 6.4 Forced Vibration of Self-excited Oscillator; 6.5 Exercises; Coupled Oscillators; 7.1 Conservative Oscillators; 7.2 Bifurcation of Nonlinear Normal Modes; 7.3 KAM Theory.
7.4 Coupled Self-excited Oscillators7.5 Exercises; NonlinearWaves; 8.1 Solitary and PeriodicWaves; 8.2 Inverse Scattering Transform; 8.3 Energy Method; 8.4 Amplitude and Slope Modulation; 8.5 Amplitude Modulations for KdV Equation; 8.6 Exercises; Notation; References; Index.
Note Print version record.
ISBN 9783319054193 (electronic bk.)
3319054198 (electronic bk.)
331905418X (print)
9783319054186 (print)
ISBN/ISSN 10.1007/978-3-319-05419-3
OCLC # 872566204
Additional Format Printed edition: 9783319054186

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