000 04030nam a22005295i 4500
001 978-3-642-22404-1
003 DE-He213
005 20140220083259.0
007 cr nn 008mamaa
008 110924s2012 gw | s |||| 0|eng d
020 _a9783642224041
_9978-3-642-22404-1
024 7 _a10.1007/978-3-642-22404-1
_2doi
050 4 _aTA355
050 4 _aTA352-356
072 7 _aTGMD4
_2bicssc
072 7 _aTEC009070
_2bisacsh
072 7 _aSCI018000
_2bisacsh
082 0 4 _a620
_223
100 1 _aLe, Khanh Chau.
_eauthor.
245 1 0 _aEnergy Methods in Dynamics
_h[electronic resource] /
_cby Khanh Chau Le.
264 1 _aBerlin, Heidelberg :
_bSpringer Berlin Heidelberg,
_c2012.
300 _aX, 294p. 142 illus.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aInteraction of Mechanics and Mathematics,
_x1860-6245
505 0 _aI 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.
520 _aThe 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, Kolmogorov-Arnold-Moser (KAM), and Whitham are derivable from this variational-asymptotic analysis.   This book grew up from the lectures given by the author in the last decade at the Ruhr University Bochum, Germany. Since vibrations and waves are constituents of various disciplines (physics, mechanics, electrical engineering etc.) and cannot be handled in a single textbook, I have restricted myself mainly to vibrations and waves of mechanical nature. The material of this book can be recommended for a one year course in higher dynamics for graduate students of mechanical and civil engineering. For this circle of readers, the emphasis is made on the constructive methods of solution and not on the rigorous mathematical proofs of convergence. As compensation, various numerical simulations of the exact and approximate solutions are provided which demonstrate vividly the validity of the used methods. To help students become more proficient, each chapter ends with exercises, of which some can be solved effectively by using Mathematica. 
650 0 _aEngineering.
650 0 _aDifferentiable dynamical systems.
650 0 _aPhysics.
650 0 _aEngineering mathematics.
650 0 _aVibration.
650 1 4 _aEngineering.
650 2 4 _aVibration, Dynamical Systems, Control.
650 2 4 _aAppl.Mathematics/Computational Methods of Engineering.
650 2 4 _aDynamical Systems and Ergodic Theory.
650 2 4 _aComplexity.
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9783642224034
830 0 _aInteraction of Mechanics and Mathematics,
_x1860-6245
856 4 0 _uhttp://dx.doi.org/10.1007/978-3-642-22404-1
912 _aZDB-2-ENG
999 _c102053
_d102053