LEADER 05076nam 22007575 450 001 9910299709403321 005 20200704035827.0 010 $a3-319-05419-8 024 7 $a10.1007/978-3-319-05419-3 035 $a(CKB)3710000000092741 035 $a(EBL)1782232 035 $a(SSID)ssj0001186872 035 $a(PQKBManifestationID)11671256 035 $a(PQKBTitleCode)TC0001186872 035 $a(PQKBWorkID)11243745 035 $a(PQKB)11485431 035 $a(MiAaPQ)EBC1782232 035 $a(DE-He213)978-3-319-05419-3 035 $a(PPN)17782543X 035 $a(EXLCZ)993710000000092741 100 $a20140304d2014 u| 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aEnergy Methods in Dynamics /$fby Khanh Chau Le, Lu Trong Khiem Nguyen 205 $a2nd ed. 2014. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2014. 215 $a1 online resource (419 p.) 225 1 $aInteraction of Mechanics and Mathematics,$x1860-6245 300 $aDescription based upon print version of record. 311 $a1-322-13453-7 311 $a3-319-05418-X 320 $aIncludes bibliographical references and index. 327 $aPreface 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 327 $a4.2 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 327 $a7.4 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 330 $aEnergy Methods in Dynamics is a textbook based on the lectures given by the first author at Ruhr University Bochum, Germany. Its aim is to help students acquire both a good grasp of the first principles from which the governing equations can be derived, and the adequate mathematical methods for their solving. Its distinctive features, as seen from the title, lie in the systematic and intensive use of Hamilton's variational principle and its generalizations for deriving the governing equations of conservative and dissipative mechanical systems, and also in providing the direct variational-asymptotic analysis, whenever available, of the energy and dissipation for the solution of these equations. It demonstrates that many well-known methods in dynamics like those of Lindstedt-Poincare, Bogoliubov-Mitropolsky, Kolmogorov-Arnold-Moser (KAM), Wentzel?Kramers?Brillouin (WKB),  and Whitham are derivable from this variational-asymptotic analysis.   This second edition includes the solutions to all exercises as well as some new materials concerning amplitude and slope modulations of nonlinear dispersive waves. 410 0$aInteraction of Mechanics and Mathematics,$x1860-6245 606 $aVibration 606 $aDynamics 606 $aDynamics 606 $aSystem theory 606 $aEnergy 606 $aVibration, Dynamical Systems, Control$3https://scigraph.springernature.com/ontologies/product-market-codes/T15036 606 $aSystems Theory, Control$3https://scigraph.springernature.com/ontologies/product-market-codes/M13070 606 $aEnergy, general$3https://scigraph.springernature.com/ontologies/product-market-codes/100000 615 0$aVibration. 615 0$aDynamics. 615 0$aDynamics. 615 0$aSystem theory. 615 0$aEnergy. 615 14$aVibration, Dynamical Systems, Control. 615 24$aSystems Theory, Control. 615 24$aEnergy, general. 676 $a003.85 700 $aLe$b Khanh Chau$4aut$4http://id.loc.gov/vocabulary/relators/aut$0924568 702 $aNguyen$b Lu Trong Khiem$4aut$4http://id.loc.gov/vocabulary/relators/aut 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910299709403321 996 $aEnergy Methods in Dynamics$92075392 997 $aUNINA