Bifurcation dynamics of a damped parametric pendulum /
By: Guo, Yu [author.].
Contributor(s): Luo, Albert C. J [author.].
Material type:
BookSeries: Synthesis digital library of engineering and computer science: ; Synthesis lectures on mechanical engineering: #22.Publisher: [San Rafael, California] : Morgan & Claypool, [2020]Description: 1 PDF (xiv, 84 pages) : illustrations (some color).Content type: text Media type: electronic Carrier type: online resourceISBN: 9781681736853.Subject(s): Pendulum | Bifurcation theory | parametric pendulum | bifurcation trees to chaos | periodic motions | frequency-amplitude characteristics | non-travelable periodic motion | travelable periodic motionsGenre/Form: Electronic books.DDC classification: 003/.857 Online resources: Abstract with links to resource | Abstract with links to full text Also available in print.| Item type | Current location | Call number | Status | Date due | Barcode | Item holds |
|---|---|---|---|---|---|---|
E books
|
PK Kelkar Library, IIT Kanpur | Available | EBKE900 |
Mode of access: World Wide Web.
System requirements: Adobe Acrobat Reader.
Part of: Synthesis digital library of engineering and computer science.
Includes bibliographical references (pages 77-82).
1. Introduction -- 2. A semi-analytical method -- 3. Discretization of a parametric pendulum -- 3.1. Implicit discrete mappings -- 3.2. Period-1 motions -- 3.3. Period-m motions
4. Bifurcation trees -- 4.1. Period-1 static points to chaos -- 4.2. Period-1 and period-3 motions to chaos -- 4.3. Independent period-2 motions to chaos -- 4.4. Independent period-4 motions to chaos -- 4.5. Period-5 and period-6 motions to chaos -- 4.6. Independent period-8, period-10, and period-12 motions
5. Harmonic frequency-amplitude characteristics -- 5.1. Discrete fourier series -- 5.2. Non-travelable period-1 static points to chaos -- 5.3. Travelable period-1 motions to chaos -- 5.4. Non-travelable period-2 motions to chaos -- 5.5. Period-3 motions -- 5.6. Period-4 motions
6. Non-travelable periodic motions -- 6.1. Librational periodic motions -- 6.2. Rotational periodic motions
7. Travelable periodic motions -- 7.1. Travelable period-1 to period-4 motions -- 7.2. Travelable period-3 to period-6 motions -- 7.3. Travelable period-5 motions.
Abstract freely available; full-text restricted to subscribers or individual document purchasers.
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The 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-m motions to chaos (m = 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.
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Title from PDF title page (viewed on December 23, 2019).
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