Resonance and bifurcation to chaos in pendulum:
"A periodically forced mathematical pendulum is one of the typical and popular nonlinear oscillators that possess complex and rich dynamical behaviors. Although the pendulum is one of the simplest nonlinear oscillators, yet, until now, we are still not able to undertake a systematical study of...
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| Format: | Elektronisch E-Book |
| Sprache: | English |
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Singapore
World Scientific Publishing Co. Pte Ltd.
© 2018
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| Online-Zugang: | Volltext |
| Zusammenfassung: | "A periodically forced mathematical pendulum is one of the typical and popular nonlinear oscillators that possess complex and rich dynamical behaviors. Although the pendulum is one of the simplest nonlinear oscillators, yet, until now, we are still not able to undertake a systematical study of periodic motions to chaos in such a simplest system due to lack of suitable mathematical methods and computational tools. To understand periodic motions and chaos in the periodically forced pendulum, the perturbation method has been adopted. One could use the Taylor series to expend the sinusoidal function to the polynomial nonlinear terms, followed by traditional perturbation methods to obtain the periodic motions of the approximated differential system. This book discusses Hamiltonian chaos and periodic motions to chaos in pendulums. This book first detects and discovers chaos in resonant layers and bifurcation trees of periodic motions to chaos in pendulum in the comprehensive fashion, which is a base to understand the behaviors of nonlinear dynamical systems, as a results of Hamiltonian chaos in the resonant layers and bifurcation trees of periodic motions to chaos. The bifurcation trees of travelable and non-travelable periodic motions to chaos will be presented through the periodically forced pendulum."-- |
| Beschreibung: | Description based on online resource; title from PDF title page (viewed January 23, 2018) |
| Beschreibung: | 1 Online-Ressource (251 Seiten) Illustrationen |
| ISBN: | 9789813231689 |
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| 500 | |a Description based on online resource; title from PDF title page (viewed January 23, 2018) | ||
| 520 | |a "A periodically forced mathematical pendulum is one of the typical and popular nonlinear oscillators that possess complex and rich dynamical behaviors. Although the pendulum is one of the simplest nonlinear oscillators, yet, until now, we are still not able to undertake a systematical study of periodic motions to chaos in such a simplest system due to lack of suitable mathematical methods and computational tools. To understand periodic motions and chaos in the periodically forced pendulum, the perturbation method has been adopted. One could use the Taylor series to expend the sinusoidal function to the polynomial nonlinear terms, followed by traditional perturbation methods to obtain the periodic motions of the approximated differential system. This book discusses Hamiltonian chaos and periodic motions to chaos in pendulums. This book first detects and discovers chaos in resonant layers and bifurcation trees of periodic motions to chaos in pendulum in the comprehensive fashion, which is a base to understand the behaviors of nonlinear dynamical systems, as a results of Hamiltonian chaos in the resonant layers and bifurcation trees of periodic motions to chaos. The bifurcation trees of travelable and non-travelable periodic motions to chaos will be presented through the periodically forced pendulum."-- | ||
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| 650 | 4 | |a Hamiltonian systems | |
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Datensatz im Suchindex
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| author | Luo, Albert C. J. |
| author_facet | Luo, Albert C. J. |
| author_role | aut |
| author_sort | Luo, Albert C. J. |
| author_variant | a c j l acj acjl |
| building | Verbundindex |
| bvnumber | BV047124599 |
| collection | ZDB-124-WOP |
| ctrlnum | (ZDB-124-WOP)00010752 (OCoLC)1237587217 (DE-599)BVBBV047124599 |
| dewey-full | 531.324 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 531 - Classical mechanics |
| dewey-raw | 531.324 |
| dewey-search | 531.324 |
| dewey-sort | 3531.324 |
| dewey-tens | 530 - Physics |
| discipline | Physik |
| discipline_str_mv | Physik |
| format | Electronic eBook |
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| id | DE-604.BV047124599 |
| illustrated | Not Illustrated |
| index_date | 2024-07-03T16:30:25Z |
| indexdate | 2024-07-10T09:03:19Z |
| institution | BVB |
| isbn | 9789813231689 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-032530839 |
| oclc_num | 1237587217 |
| open_access_boolean | |
| physical | 1 Online-Ressource (251 Seiten) Illustrationen |
| psigel | ZDB-124-WOP |
| publishDate | 2018 |
| publishDateSearch | 2018 |
| publishDateSort | 2018 |
| publisher | World Scientific Publishing Co. Pte Ltd. |
| record_format | marc |
| spelling | Luo, Albert C. J. Verfasser aut Resonance and bifurcation to chaos in pendulum Albert C. J. Luo Singapore World Scientific Publishing Co. Pte Ltd. © 2018 1 Online-Ressource (251 Seiten) Illustrationen txt rdacontent c rdamedia cr rdacarrier Description based on online resource; title from PDF title page (viewed January 23, 2018) "A periodically forced mathematical pendulum is one of the typical and popular nonlinear oscillators that possess complex and rich dynamical behaviors. Although the pendulum is one of the simplest nonlinear oscillators, yet, until now, we are still not able to undertake a systematical study of periodic motions to chaos in such a simplest system due to lack of suitable mathematical methods and computational tools. To understand periodic motions and chaos in the periodically forced pendulum, the perturbation method has been adopted. One could use the Taylor series to expend the sinusoidal function to the polynomial nonlinear terms, followed by traditional perturbation methods to obtain the periodic motions of the approximated differential system. This book discusses Hamiltonian chaos and periodic motions to chaos in pendulums. This book first detects and discovers chaos in resonant layers and bifurcation trees of periodic motions to chaos in pendulum in the comprehensive fashion, which is a base to understand the behaviors of nonlinear dynamical systems, as a results of Hamiltonian chaos in the resonant layers and bifurcation trees of periodic motions to chaos. The bifurcation trees of travelable and non-travelable periodic motions to chaos will be presented through the periodically forced pendulum."-- Pendulum Chaotic behavior in systems Hamiltonian systems Electronic books http://www.worldscientific.com/worldscibooks/10.1142/10752#t=toc Verlag URL des Erstveröffentlichers Volltext |
| spellingShingle | Luo, Albert C. J. Resonance and bifurcation to chaos in pendulum Pendulum Chaotic behavior in systems Hamiltonian systems Electronic books |
| title | Resonance and bifurcation to chaos in pendulum |
| title_auth | Resonance and bifurcation to chaos in pendulum |
| title_exact_search | Resonance and bifurcation to chaos in pendulum |
| title_exact_search_txtP | Resonance and bifurcation to chaos in pendulum |
| title_full | Resonance and bifurcation to chaos in pendulum Albert C. J. Luo |
| title_fullStr | Resonance and bifurcation to chaos in pendulum Albert C. J. Luo |
| title_full_unstemmed | Resonance and bifurcation to chaos in pendulum Albert C. J. Luo |
| title_short | Resonance and bifurcation to chaos in pendulum |
| title_sort | resonance and bifurcation to chaos in pendulum |
| topic | Pendulum Chaotic behavior in systems Hamiltonian systems Electronic books |
| topic_facet | Pendulum Chaotic behavior in systems Hamiltonian systems Electronic books |
| url | http://www.worldscientific.com/worldscibooks/10.1142/10752#t=toc |
| work_keys_str_mv | AT luoalbertcj resonanceandbifurcationtochaosinpendulum |