000 | 03974nam a22005655i 4500 | ||
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001 | 978-3-031-79645-6 | ||
003 | DE-He213 | ||
005 | 20240730164134.0 | ||
007 | cr nn 008mamaa | ||
008 | 220601s2020 sz | s |||| 0|eng d | ||
020 |
_a9783031796456 _9978-3-031-79645-6 |
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024 | 7 |
_a10.1007/978-3-031-79645-6 _2doi |
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050 | 4 | _aT1-995 | |
072 | 7 |
_aTBC _2bicssc |
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_aTEC000000 _2bisacsh |
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072 | 7 |
_aTBC _2thema |
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082 | 0 | 4 |
_a620 _223 |
100 | 1 |
_aGuo, Yu. _eauthor. _4aut _4http://id.loc.gov/vocabulary/relators/aut _982324 |
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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. |
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300 |
_aXIV, 84 p. _bonline resource. |
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336 |
_atext _btxt _2rdacontent |
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337 |
_acomputer _bc _2rdamedia |
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338 |
_aonline resource _bcr _2rdacarrier |
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347 |
_atext file _bPDF _2rda |
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490 | 1 |
_aSynthesis Lectures on Mechanical Engineering, _x2573-3176 |
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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 |
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650 | 0 |
_aElectrical engineering. _982325 |
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650 | 0 |
_aEngineering design. _93802 |
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650 | 0 |
_aMicrotechnology. _928219 |
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650 | 0 |
_aMicroelectromechanical systems. _96063 |
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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 |
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710 | 2 |
_aSpringerLink (Online service) _982330 |
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_iPrinted edition: _z9783031796463 |
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_iPrinted edition: _z9783031796449 |
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_iPrinted edition: _z9783031796470 |
830 | 0 |
_aSynthesis Lectures on Mechanical Engineering, _x2573-3176 _982331 |
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