000 03974nam a22005655i 4500
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008 220601s2020 sz | s |||| 0|eng d
020 _a9783031796456
_9978-3-031-79645-6
024 7 _a10.1007/978-3-031-79645-6
_2doi
050 4 _aT1-995
072 7 _aTBC
_2bicssc
072 7 _aTEC000000
_2bisacsh
072 7 _aTBC
_2thema
082 0 4 _a620
_223
100 1 _aGuo, Yu.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
_982324
245 1 0 _aBifurcation Dynamics of a Damped Parametric Pendulum
_h[electronic resource] /
_cby Yu Guo, Albert C.J. Luo.
250 _a1st ed. 2020.
264 1 _aCham :
_bSpringer International Publishing :
_bImprint: Springer,
_c2020.
300 _aXIV, 84 p.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aSynthesis Lectures on Mechanical Engineering,
_x2573-3176
505 0 _aPreface -- Introduction -- A Semi-Analytical Method -- Discretization of a Parametric Pendulum -- Bifurcation Trees -- Harmonic Frequency-Amplitude Characteristics -- Non-Travelable Periodic Motions -- Travelable Periodic Motions -- References -- Authors' Biographies.
520 _aThe inherent complex dynamics of a parametrically excited pendulum is of great interest in nonlinear dynamics, which can help one better understand the complex world. Even though the parametrically excited pendulum is one of the simplest nonlinear systems, until now, complex motions in such a parametric pendulum cannot be achieved. In this book, the bifurcation dynamics of periodic motions to chaos in a damped, parametrically excited pendulum is discussed. Complete bifurcation trees of periodic motions to chaos in the parametrically excited pendulum include: period-1 motion (static equilibriums) to chaos, and period-���� motions to chaos (���� = 1, 2, ···, 6, 8, ···, 12). The aforesaid bifurcation trees of periodic motions to chaos coexist in the same parameter ranges, which are very difficult to determine through traditional analysis. Harmonic frequency-amplitude characteristics of such bifurcation trees are also presented to show motion complexity and nonlinearity in such a parametrically excited pendulum system. The non-travelable and travelable periodic motions on the bifurcation trees are discovered. Through the bifurcation trees of travelable and non-travelable periodic motions, the travelable and non-travelable chaos in the parametrically excited pendulum can be achieved. Based on the traditional analysis, one cannot achieve the adequate solutions presented herein for periodic motions to chaos in the parametrically excited pendulum. The results in this book may cause one rethinking how to determine motion complexity in nonlinear dynamical systems.
650 0 _aEngineering.
_99405
650 0 _aElectrical engineering.
_982325
650 0 _aEngineering design.
_93802
650 0 _aMicrotechnology.
_928219
650 0 _aMicroelectromechanical systems.
_96063
650 1 4 _aTechnology and Engineering.
_982326
650 2 4 _aElectrical and Electronic Engineering.
_982327
650 2 4 _aEngineering Design.
_93802
650 2 4 _aMicrosystems and MEMS.
_982328
700 1 _aLuo, Albert C.J.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
_982329
710 2 _aSpringerLink (Online service)
_982330
773 0 _tSpringer Nature eBook
776 0 8 _iPrinted edition:
_z9783031796463
776 0 8 _iPrinted edition:
_z9783031796449
776 0 8 _iPrinted edition:
_z9783031796470
830 0 _aSynthesis Lectures on Mechanical Engineering,
_x2573-3176
_982331
856 4 0 _uhttps://doi.org/10.1007/978-3-031-79645-6
912 _aZDB-2-SXSC
942 _cEBK
999 _c85338
_d85338