| Description |
1 online resource (xiii, 142 pages) : illustrations |
| Physical Medium |
polychrome |
| Description |
text file |
| Bibliography |
Includes bibliographical references (pages 133-138) and index. |
| 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. |
| Summary |
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. |
| Access |
Use copy Restrictions unspecified MiAaHDL |
| Reproduction |
Electronic reproduction. [S.l.] : HathiTrust Digital Library, 2011. MiAaHDL |
| System Details |
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 |
| Processing Action |
digitized 2011 HathiTrust Digital Library committed to preserve MiAaHDL |
| Local Note |
eBooks on EBSCOhost EBSCO eBook Subscription Academic Collection - North America |
| Subject |
Pendulum.
|
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Pendulum. |
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Chaotic behavior in systems.
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Chaotic behavior in systems. |
| Genre/Form |
Electronic books.
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Electronic books.
|
| Other Form: |
Print version: Gitterman, M. Chaotic pendulum. Singapore ; Hackensack, NJ ; London : World Scientific, ©2010 9789814322003 (DLC) 2011281759 (OCoLC)613430898 |
| ISBN |
9789814322010 (electronic book) |
|
9814322016 (electronic book) |
|
1283144948 |
|
9781283144940 |
|
9789814322003 |
|
9814322008 |
|
