Smooth and nonsmooth high dimensional chaos and the melnikov-type methods /:
This book focuses on the development of Melnikov-type methods applied to high dimensional dynamical systems governed by ordinary differential equations. Although the classical Melnikov's technique has found various applications in predicting homoclinic intersections, it is devoted only to the a...
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| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Singapore ; Hackensack, NJ :
World Scientific,
©2007.
|
| Schriftenreihe: | World Scientific series on nonlinear science. Monographs and treatises ;
v. 60. |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Zusammenfassung: | This book focuses on the development of Melnikov-type methods applied to high dimensional dynamical systems governed by ordinary differential equations. Although the classical Melnikov's technique has found various applications in predicting homoclinic intersections, it is devoted only to the analysis of three-dimensional systems (in the case of mechanics, they represent one-degree-of-freedom nonautonomous systems). This book extends the classical Melnikov's approach to the study of high dimensional dynamical systems, and uses simple models of dry friction to analytically predict the occurrenc. |
| Beschreibung: | 1 online resource (x, 307 pages :) |
| Bibliographie: | Includes bibliographical references (pages 285-289) and index. |
| ISBN: | 9789812709103 981270910X |
Internformat
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| 588 | 0 | |a Print version record. | |
| 520 | |a This book focuses on the development of Melnikov-type methods applied to high dimensional dynamical systems governed by ordinary differential equations. Although the classical Melnikov's technique has found various applications in predicting homoclinic intersections, it is devoted only to the analysis of three-dimensional systems (in the case of mechanics, they represent one-degree-of-freedom nonautonomous systems). This book extends the classical Melnikov's approach to the study of high dimensional dynamical systems, and uses simple models of dry friction to analytically predict the occurrenc. | ||
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| author | Awrejcewicz, J. (Jan) |
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| contents | 1. A role of the Melnikov-type methods in applied sciences -- 2. Classical Melnikov approach -- 3. Homoclinic chaos criterion in a rotated froude pendulum with dry fiction -- 4. Smooth and nonsmooth dynamics of a 1uasi-autonomous oscillator with coulomb and viscous frictions -- 5. Application of the Melnikov-Gruendler method to mechanical systems -- 6. A self-excited spherical pendulum -- 7. A double self-excited duffing-type oscillator -- 8. A triple self-excited duffing-type oscillator. |
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| illustrated | Illustrated |
| indexdate | 2024-10-25T16:16:56Z |
| institution | BVB |
| isbn | 9789812709103 981270910X |
| language | English |
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| series | World Scientific series on nonlinear science. Monographs and treatises ; |
| series2 | World Scientific series on nonlinear science. Series A ; |
| spelling | Awrejcewicz, J. (Jan) https://id.oclc.org/worldcat/entity/E39PBJr83fkjVcwR6tgHmDBHG3 http://id.loc.gov/authorities/names/n88212452 Smooth and nonsmooth high dimensional chaos and the melnikov-type methods / Jan Awrejcewicz, Mariusz M. Holicke. Singapore ; Hackensack, NJ : World Scientific, ©2007. 1 online resource (x, 307 pages :) text txt rdacontent computer c rdamedia online resource cr rdacarrier World Scientific series on nonlinear science. Series A ; v. 60 Includes bibliographical references (pages 285-289) and index. 1. A role of the Melnikov-type methods in applied sciences -- 2. Classical Melnikov approach -- 3. Homoclinic chaos criterion in a rotated froude pendulum with dry fiction -- 4. Smooth and nonsmooth dynamics of a 1uasi-autonomous oscillator with coulomb and viscous frictions -- 5. Application of the Melnikov-Gruendler method to mechanical systems -- 6. A self-excited spherical pendulum -- 7. A double self-excited duffing-type oscillator -- 8. A triple self-excited duffing-type oscillator. Print version record. This book focuses on the development of Melnikov-type methods applied to high dimensional dynamical systems governed by ordinary differential equations. Although the classical Melnikov's technique has found various applications in predicting homoclinic intersections, it is devoted only to the analysis of three-dimensional systems (in the case of mechanics, they represent one-degree-of-freedom nonautonomous systems). This book extends the classical Melnikov's approach to the study of high dimensional dynamical systems, and uses simple models of dry friction to analytically predict the occurrenc. Chaotic behavior in systems. http://id.loc.gov/authorities/subjects/sh85022562 Differentiable dynamical systems. http://id.loc.gov/authorities/subjects/sh85037882 Nonlinear oscillators. http://id.loc.gov/authorities/subjects/sh85092330 Chaos. Dynamique différentiable. Oscillateurs non linéaires. SCIENCE Chaotic Behavior in Systems. bisacsh Chaotic behavior in systems fast Differentiable dynamical systems fast Nonlinear oscillators fast Holicke, Mariusz M. https://id.oclc.org/worldcat/entity/E39PCjMq9DrdywjPxYqmjMbdpP http://id.loc.gov/authorities/names/no2008134407 has work: Smooth and nonsmooth high dimensional chaos and the melnikov-type methods (Text) https://id.oclc.org/worldcat/entity/E39PCGHyJ7yrckBW4x8CRKH7Xm https://id.oclc.org/worldcat/ontology/hasWork Print version: Awrejcewicz, J. (Jan). Smooth and nonsmooth high dimensional chaos and the melnikov-type methods. Singapore ; Hackensack, NJ : World Scientific, ©2007 9812709096 9789812709097 (DLC) 2008295967 (OCoLC)170923078 World Scientific series on nonlinear science. Series A, Monographs and treatises ; v. 60. http://id.loc.gov/authorities/names/no94008495 FWS01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=235966 Volltext CBO01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=235966 Volltext |
| spellingShingle | Awrejcewicz, J. (Jan) Smooth and nonsmooth high dimensional chaos and the melnikov-type methods / World Scientific series on nonlinear science. Monographs and treatises ; 1. A role of the Melnikov-type methods in applied sciences -- 2. Classical Melnikov approach -- 3. Homoclinic chaos criterion in a rotated froude pendulum with dry fiction -- 4. Smooth and nonsmooth dynamics of a 1uasi-autonomous oscillator with coulomb and viscous frictions -- 5. Application of the Melnikov-Gruendler method to mechanical systems -- 6. A self-excited spherical pendulum -- 7. A double self-excited duffing-type oscillator -- 8. A triple self-excited duffing-type oscillator. Chaotic behavior in systems. http://id.loc.gov/authorities/subjects/sh85022562 Differentiable dynamical systems. http://id.loc.gov/authorities/subjects/sh85037882 Nonlinear oscillators. http://id.loc.gov/authorities/subjects/sh85092330 Chaos. Dynamique différentiable. Oscillateurs non linéaires. SCIENCE Chaotic Behavior in Systems. bisacsh Chaotic behavior in systems fast Differentiable dynamical systems fast Nonlinear oscillators fast |
| subject_GND | http://id.loc.gov/authorities/subjects/sh85022562 http://id.loc.gov/authorities/subjects/sh85037882 http://id.loc.gov/authorities/subjects/sh85092330 |
| title | Smooth and nonsmooth high dimensional chaos and the melnikov-type methods / |
| title_auth | Smooth and nonsmooth high dimensional chaos and the melnikov-type methods / |
| title_exact_search | Smooth and nonsmooth high dimensional chaos and the melnikov-type methods / |
| title_full | Smooth and nonsmooth high dimensional chaos and the melnikov-type methods / Jan Awrejcewicz, Mariusz M. Holicke. |
| title_fullStr | Smooth and nonsmooth high dimensional chaos and the melnikov-type methods / Jan Awrejcewicz, Mariusz M. Holicke. |
| title_full_unstemmed | Smooth and nonsmooth high dimensional chaos and the melnikov-type methods / Jan Awrejcewicz, Mariusz M. Holicke. |
| title_short | Smooth and nonsmooth high dimensional chaos and the melnikov-type methods / |
| title_sort | smooth and nonsmooth high dimensional chaos and the melnikov type methods |
| topic | Chaotic behavior in systems. http://id.loc.gov/authorities/subjects/sh85022562 Differentiable dynamical systems. http://id.loc.gov/authorities/subjects/sh85037882 Nonlinear oscillators. http://id.loc.gov/authorities/subjects/sh85092330 Chaos. Dynamique différentiable. Oscillateurs non linéaires. SCIENCE Chaotic Behavior in Systems. bisacsh Chaotic behavior in systems fast Differentiable dynamical systems fast Nonlinear oscillators fast |
| topic_facet | Chaotic behavior in systems. Differentiable dynamical systems. Nonlinear oscillators. Chaos. Dynamique différentiable. Oscillateurs non linéaires. SCIENCE Chaotic Behavior in Systems. Chaotic behavior in systems Differentiable dynamical systems Nonlinear oscillators |
| url | https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=235966 |
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