000 04215nam a22006015i 4500
001 978-3-662-53094-8
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008 160927s2017 gw | s |||| 0|eng d
020 _a9783662530948
_9978-3-662-53094-8
024 7 _a10.1007/978-3-662-53094-8
_2doi
050 4 _aTA352-356
072 7 _aTGMD4
_2bicssc
072 7 _aTEC009070
_2bisacsh
072 7 _aTGMD
_2thema
082 0 4 _a620.3
_223
100 1 _aCao, Qingjie.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
_957704
245 1 2 _aA Smooth and Discontinuous Oscillator
_h[electronic resource] :
_bTheory, Methodology and Applications /
_cby Qingjie Cao, Alain Léger.
250 _a1st ed. 2017.
264 1 _aBerlin, Heidelberg :
_bSpringer Berlin Heidelberg :
_bImprint: Springer,
_c2017.
300 _aXIX, 262 p. 131 illus., 54 illus. in color.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aSpringer Tracts in Mechanical Engineering,
_x2195-9870
505 0 _aBackground: Nonlinear Systems -- An Smooth and Discontinuous (SD) Oscillator -- Bifurcation Behaviour -- Periodic Motions of the Perturbed SD Oscillator -- The Exact Solutions -- Chaotic Motions of the SD Oscillator -- Experimental Investigation of the SD Oscillator -- Applications in Structural Dynamics -- Applications in Engineering Isolation -- Challenges and the Open Problems.
520 _aThis is the first book to introduce the irrational elliptic function series, providing a theoretical treatment for the smooth and discontinuous system and opening a new branch of applied mathematics. The discovery of the smooth and discontinuous (SD) oscillator and the SD attractors discussed in this book represents a further milestone in nonlinear dynamics, following on the discovery of the Ueda attractor in 1961 and Lorenz attractor in 1963. This particular system bears significant similarities to the Duffing oscillator, exhibiting the standard dynamics governed by the hyperbolic structure associated with the stationary state of the double well. However, there is a substantial departure in nonlinear dynamics from standard dynamics at the discontinuous stage. The constructed irrational elliptic function series, which offers a way to directly approach the nature dynamics analytically for both smooth and discontinuous behaviours including the unperturbed periodic motions and th e perturbed chaotic attractors without any truncation, is of particular interest. Readers will also gain a deeper understanding of the actual nonlinear phenomena by means of a simple mechanical model: the theory, methodology, and the applications in various interlinked disciplines of sciences and engineering. This book offers a valuable resource for researchers, professionals and postgraduate students in mechanical engineering, non-linear dynamics, and related areas, such as nonlinear modelling in various fields of mathematics, physics and the engineering sciences.
650 0 _aMultibody systems.
_96018
650 0 _aVibration.
_96645
650 0 _aMechanics, Applied.
_93253
650 0 _aNonlinear Optics.
_911414
650 0 _aMechanics.
_98758
650 0 _aMathematical models.
_94632
650 1 4 _aMultibody Systems and Mechanical Vibrations.
_932157
650 2 4 _aNonlinear Optics.
_911414
650 2 4 _aClassical Mechanics.
_931661
650 2 4 _aMathematical Modeling and Industrial Mathematics.
_933097
700 1 _aLéger, Alain.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
_957705
710 2 _aSpringerLink (Online service)
_957706
773 0 _tSpringer Nature eBook
776 0 8 _iPrinted edition:
_z9783662530924
776 0 8 _iPrinted edition:
_z9783662530931
776 0 8 _iPrinted edition:
_z9783662571101
830 0 _aSpringer Tracts in Mechanical Engineering,
_x2195-9870
_957707
856 4 0 _uhttps://doi.org/10.1007/978-3-662-53094-8
912 _aZDB-2-ENG
912 _aZDB-2-SXE
942 _cEBK
999 _c79999
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