The chaotic pendulum /:
Pendulum is the simplest nonlinear system, which, however, provides the means for the description of different phenomena in Nature that occur in physics, chemistry, biology, medicine, communications, economics and sociology. The chaotic behavior of pendulum is usually associated with the random forc...
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| Format: | Elektronisch E-Book |
| Sprache: | English |
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Singapore ; Hackensack, NJ ; London :
World Scientific,
©2010.
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| Online-Zugang: | Volltext |
| Zusammenfassung: | Pendulum is the simplest nonlinear system, which, however, provides the means for the description of different phenomena in Nature that occur in physics, chemistry, biology, medicine, communications, economics and sociology. The chaotic behavior of pendulum is usually associated with the random force acting on a pendulum (Brownian motion). Another type of chaotic motion (deterministic chaos) occurs in nonlinear systems with only few degrees of freedom. This book presents a comprehensive description of these phenomena going on in underdamped and overdamped pendula subject to additive and multiplicative periodic and random forces. No preliminary knowledge, such as complex mathematical or numerical methods, is required from a reader other than undergraduate courses in mathematical physics. A wide group of researchers, along with students and teachers will, thus, benefit from this definitive book on nonlinear dynamics. |
| Beschreibung: | 1 online resource (xiii, 142 pages) : illustrations |
| Format: | Master and use copy. Digital master created according to Benchmark for Faithful Digital Reproductions of Monographs and Serials, Version 1. Digital Library Federation, December 2002. |
| Bibliographie: | Includes bibliographical references (pages 133-138) and index. |
| ISBN: | 9789814322010 9814322016 1283144948 9781283144940 9786613144942 6613144940 |
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| 245 | 1 | 4 | |a The chaotic pendulum / |c Moshe Gitterman. |
| 260 | |a Singapore ; |a Hackensack, NJ ; |a London : |b World Scientific, |c ©2010. | ||
| 300 | |a 1 online resource (xiii, 142 pages) : |b illustrations | ||
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| 504 | |a Includes bibliographical references (pages 133-138) and index. | ||
| 505 | 0 | |a 1. Pendulum equations. 1.1. Mathematical pendulum. 1.2. Period of oscillations. 1.3. Underdamped pendulum. 1.4. Nonlinear vs linear equation. 1.5. Isomorphic models. 1.6. General concepts -- 2. Deterministic chaos. 2.1. Damped, periodically driven pendulum. 2.2. Analytic methods. 2.3. Parametric periodic force. 2.4. Parametrically driven pendulum. 2.5. Periodic and constant forces. 2.6. Parametric and constant forces. 2.7. External and parametric periodic forces -- 3. Pendulum subject to a random force. 3.1. Noise. 3.2. External random force. 3.3. Constant and random forces. 3.4. External periodic and random forces. 3.5. Pendulum with multiplicative noise. 3.6. Parametric periodic and random forces. 3.7. Damped pendulum subject to a constant torque, periodic force and noise. 3.8. Overdamped pendulum -- 4. Systems with two degrees of freedom. 4.1. Spring pendulum. 4.2. Double pendulum. 4.3. Spherical pendulum -- 5. Conclusions. | |
| 520 | |a Pendulum is the simplest nonlinear system, which, however, provides the means for the description of different phenomena in Nature that occur in physics, chemistry, biology, medicine, communications, economics and sociology. The chaotic behavior of pendulum is usually associated with the random force acting on a pendulum (Brownian motion). Another type of chaotic motion (deterministic chaos) occurs in nonlinear systems with only few degrees of freedom. This book presents a comprehensive description of these phenomena going on in underdamped and overdamped pendula subject to additive and multiplicative periodic and random forces. No preliminary knowledge, such as complex mathematical or numerical methods, is required from a reader other than undergraduate courses in mathematical physics. A wide group of researchers, along with students and teachers will, thus, benefit from this definitive book on nonlinear dynamics. | ||
| 588 | 0 | |a Print version record. | |
| 506 | |3 Use copy |f Restrictions unspecified |2 star |5 MiAaHDL | ||
| 533 | |a Electronic reproduction. |b [Place of publication not identified] : |c HathiTrust Digital Library, |d 2011. |5 MiAaHDL | ||
| 538 | |a Master and use copy. Digital master created according to Benchmark for Faithful Digital Reproductions of Monographs and Serials, Version 1. Digital Library Federation, December 2002. |u http://purl.oclc.org/DLF/benchrepro0212 |5 MiAaHDL | ||
| 583 | 1 | |a digitized |c 2011 |h HathiTrust Digital Library |l committed to preserve |2 pda |5 MiAaHDL | |
| 546 | |a English. | ||
| 650 | 0 | |a Pendulum. |0 http://id.loc.gov/authorities/subjects/sh85099384 | |
| 650 | 0 | |a Chaotic behavior in systems. |0 http://id.loc.gov/authorities/subjects/sh85022562 | |
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| contents | 1. Pendulum equations. 1.1. Mathematical pendulum. 1.2. Period of oscillations. 1.3. Underdamped pendulum. 1.4. Nonlinear vs linear equation. 1.5. Isomorphic models. 1.6. General concepts -- 2. Deterministic chaos. 2.1. Damped, periodically driven pendulum. 2.2. Analytic methods. 2.3. Parametric periodic force. 2.4. Parametrically driven pendulum. 2.5. Periodic and constant forces. 2.6. Parametric and constant forces. 2.7. External and parametric periodic forces -- 3. Pendulum subject to a random force. 3.1. Noise. 3.2. External random force. 3.3. Constant and random forces. 3.4. External periodic and random forces. 3.5. Pendulum with multiplicative noise. 3.6. Parametric periodic and random forces. 3.7. Damped pendulum subject to a constant torque, periodic force and noise. 3.8. Overdamped pendulum -- 4. Systems with two degrees of freedom. 4.1. Spring pendulum. 4.2. Double pendulum. 4.3. Spherical pendulum -- 5. Conclusions. |
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Pendulum equations. 1.1. Mathematical pendulum. 1.2. Period of oscillations. 1.3. Underdamped pendulum. 1.4. Nonlinear vs linear equation. 1.5. Isomorphic models. 1.6. General concepts -- 2. Deterministic chaos. 2.1. Damped, periodically driven pendulum. 2.2. Analytic methods. 2.3. Parametric periodic force. 2.4. Parametrically driven pendulum. 2.5. Periodic and constant forces. 2.6. Parametric and constant forces. 2.7. External and parametric periodic forces -- 3. Pendulum subject to a random force. 3.1. Noise. 3.2. External random force. 3.3. Constant and random forces. 3.4. External periodic and random forces. 3.5. Pendulum with multiplicative noise. 3.6. Parametric periodic and random forces. 3.7. Damped pendulum subject to a constant torque, periodic force and noise. 3.8. Overdamped pendulum -- 4. Systems with two degrees of freedom. 4.1. Spring pendulum. 4.2. Double pendulum. 4.3. Spherical pendulum -- 5. Conclusions.</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">Pendulum is the simplest nonlinear system, which, however, provides the means for the description of different phenomena in Nature that occur in physics, chemistry, biology, medicine, communications, economics and sociology. The chaotic behavior of pendulum is usually associated with the random force acting on a pendulum (Brownian motion). Another type of chaotic motion (deterministic chaos) occurs in nonlinear systems with only few degrees of freedom. This book presents a comprehensive description of these phenomena going on in underdamped and overdamped pendula subject to additive and multiplicative periodic and random forces. No preliminary knowledge, such as complex mathematical or numerical methods, is required from a reader other than undergraduate courses in mathematical physics. 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| id | ZDB-4-EBA-ocn740444827 |
| illustrated | Illustrated |
| indexdate | 2024-11-27T13:17:54Z |
| institution | BVB |
| isbn | 9789814322010 9814322016 1283144948 9781283144940 9786613144942 6613144940 |
| language | English |
| oclc_num | 740444827 |
| open_access_boolean | |
| owner | MAIN DE-863 DE-BY-FWS |
| owner_facet | MAIN DE-863 DE-BY-FWS |
| physical | 1 online resource (xiii, 142 pages) : illustrations |
| psigel | ZDB-4-EBA |
| publishDate | 2010 |
| publishDateSearch | 2010 |
| publishDateSort | 2010 |
| publisher | World Scientific, |
| record_format | marc |
| spelling | Gitterman, M. https://id.oclc.org/worldcat/entity/E39PCjxXJQhFQ3Qb6c77WfgVG3 http://id.loc.gov/authorities/names/n80130596 The chaotic pendulum / Moshe Gitterman. Singapore ; Hackensack, NJ ; London : World Scientific, ©2010. 1 online resource (xiii, 142 pages) : illustrations text txt rdacontent computer c rdamedia online resource cr rdacarrier data file Includes bibliographical references (pages 133-138) and index. 1. Pendulum equations. 1.1. Mathematical pendulum. 1.2. Period of oscillations. 1.3. Underdamped pendulum. 1.4. Nonlinear vs linear equation. 1.5. Isomorphic models. 1.6. General concepts -- 2. Deterministic chaos. 2.1. Damped, periodically driven pendulum. 2.2. Analytic methods. 2.3. Parametric periodic force. 2.4. Parametrically driven pendulum. 2.5. Periodic and constant forces. 2.6. Parametric and constant forces. 2.7. External and parametric periodic forces -- 3. Pendulum subject to a random force. 3.1. Noise. 3.2. External random force. 3.3. Constant and random forces. 3.4. External periodic and random forces. 3.5. Pendulum with multiplicative noise. 3.6. Parametric periodic and random forces. 3.7. Damped pendulum subject to a constant torque, periodic force and noise. 3.8. Overdamped pendulum -- 4. Systems with two degrees of freedom. 4.1. Spring pendulum. 4.2. Double pendulum. 4.3. Spherical pendulum -- 5. Conclusions. Pendulum is the simplest nonlinear system, which, however, provides the means for the description of different phenomena in Nature that occur in physics, chemistry, biology, medicine, communications, economics and sociology. The chaotic behavior of pendulum is usually associated with the random force acting on a pendulum (Brownian motion). Another type of chaotic motion (deterministic chaos) occurs in nonlinear systems with only few degrees of freedom. This book presents a comprehensive description of these phenomena going on in underdamped and overdamped pendula subject to additive and multiplicative periodic and random forces. No preliminary knowledge, such as complex mathematical or numerical methods, is required from a reader other than undergraduate courses in mathematical physics. A wide group of researchers, along with students and teachers will, thus, benefit from this definitive book on nonlinear dynamics. Print version record. Use copy Restrictions unspecified star MiAaHDL Electronic reproduction. [Place of publication not identified] : HathiTrust Digital Library, 2011. MiAaHDL Master and use copy. Digital master created according to Benchmark for Faithful Digital Reproductions of Monographs and Serials, Version 1. Digital Library Federation, December 2002. http://purl.oclc.org/DLF/benchrepro0212 MiAaHDL digitized 2011 HathiTrust Digital Library committed to preserve pda MiAaHDL English. Pendulum. http://id.loc.gov/authorities/subjects/sh85099384 Chaotic behavior in systems. http://id.loc.gov/authorities/subjects/sh85022562 Pendule. Chaos. SCIENCE Chaotic Behavior in Systems. bisacsh Chaotic behavior in systems fast Pendulum fast has work: The chaotic pendulum (Text) https://id.oclc.org/worldcat/entity/E39PCGkVcfQRHQ74y7MGyBMCKm https://id.oclc.org/worldcat/ontology/hasWork Print version: Gitterman, M. Chaotic pendulum. Singapore ; Hackensack, NJ ; London : World Scientific, ©2010 9789814322003 (DLC) 2011281759 (OCoLC)613430898 FWS01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=374923 Volltext |
| spellingShingle | Gitterman, M. The chaotic pendulum / 1. Pendulum equations. 1.1. Mathematical pendulum. 1.2. Period of oscillations. 1.3. Underdamped pendulum. 1.4. Nonlinear vs linear equation. 1.5. Isomorphic models. 1.6. General concepts -- 2. Deterministic chaos. 2.1. Damped, periodically driven pendulum. 2.2. Analytic methods. 2.3. Parametric periodic force. 2.4. Parametrically driven pendulum. 2.5. Periodic and constant forces. 2.6. Parametric and constant forces. 2.7. External and parametric periodic forces -- 3. Pendulum subject to a random force. 3.1. Noise. 3.2. External random force. 3.3. Constant and random forces. 3.4. External periodic and random forces. 3.5. Pendulum with multiplicative noise. 3.6. Parametric periodic and random forces. 3.7. Damped pendulum subject to a constant torque, periodic force and noise. 3.8. Overdamped pendulum -- 4. Systems with two degrees of freedom. 4.1. Spring pendulum. 4.2. Double pendulum. 4.3. Spherical pendulum -- 5. Conclusions. Pendulum. http://id.loc.gov/authorities/subjects/sh85099384 Chaotic behavior in systems. http://id.loc.gov/authorities/subjects/sh85022562 Pendule. Chaos. SCIENCE Chaotic Behavior in Systems. bisacsh Chaotic behavior in systems fast Pendulum fast |
| subject_GND | http://id.loc.gov/authorities/subjects/sh85099384 http://id.loc.gov/authorities/subjects/sh85022562 |
| title | The chaotic pendulum / |
| title_auth | The chaotic pendulum / |
| title_exact_search | The chaotic pendulum / |
| title_full | The chaotic pendulum / Moshe Gitterman. |
| title_fullStr | The chaotic pendulum / Moshe Gitterman. |
| title_full_unstemmed | The chaotic pendulum / Moshe Gitterman. |
| title_short | The chaotic pendulum / |
| title_sort | chaotic pendulum |
| topic | Pendulum. http://id.loc.gov/authorities/subjects/sh85099384 Chaotic behavior in systems. http://id.loc.gov/authorities/subjects/sh85022562 Pendule. Chaos. SCIENCE Chaotic Behavior in Systems. bisacsh Chaotic behavior in systems fast Pendulum fast |
| topic_facet | Pendulum. Chaotic behavior in systems. Pendule. Chaos. SCIENCE Chaotic Behavior in Systems. Chaotic behavior in systems Pendulum |
| url | https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=374923 |
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