| Description |
1 online resource (xi, 120 pages) : illustrations |
| Physical Medium |
monochrome |
| Description |
text file |
| Bibliography |
Includes bibliographical references (pages 113-118) and index. |
| Contents |
1. Formulation of the problem. 1.1. Mathematical pendulum. 1.2. Isomorphic models. 1.3. Noise -- 2. Overdamped pendulum. 2.1. Deterministic motion. 2.2. Influence of noise. 2.3. Periodic driven force -- 3. Underdamped pendulum. 3.1. Pendulum with constant torque. 3.2. Pendulum with multiplicative noise. 3.3. Pendulum with additive noise. 3.4. Periodically driven pendulum. 3.5. Damped pendulum subject to constant torque, periodic force and noise. 3.6. Pendulum with oscillating suspension point. 3.7. Spring pendulum. 3.8. Resonance-type phenomena -- 4. Deterministic chaos. 4.1. General concepts. 4.2. Transition to chaos. 4.3. Pendulum subject to two periodic fields -- 5. Inverted pendulum. 5.1. Oscillations of the suspension axis. 5.2. The tilted parametric pendulum. 5.3. Random vibrations of the suspension axis. 5.4. Spring pendulum. 5.5. Spring pendulum driven by a periodic force -- 6. Conclusions. |
| Summary |
This book contains the general description of the mathematical pendulum subject to constant torque, periodic and random forces. The latter appear in additive and multiplicative form with their possible correlation. For the underdamped pendulum driven by periodic forces, a new phenomenon - deterministic chaos - comes into play, and the common action of this chaos and the influence of noise are taken into account. The inverted position of the pendulum can be stabilized either by periodic or random oscillations of the suspension axis or by inserting a spring into a rigid rod, or by their combination. The pendulum is one of the simplest nonlinear models, which has many applications in physics, chemistry, biology, medicine, communications, economics and sociology. A wide group of researchers working in these fields, along with students and teachers, will benefit from this book. |
| Local Note |
eBooks on EBSCOhost EBSCO eBook Subscription Academic Collection - North America |
| Subject |
Pendulum.
|
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Pendulum. |
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Noise.
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Noise. |
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Mechanics.
|
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Mechanics. |
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Physics.
|
|
Physics. |
| Genre/Form |
Electronic books.
|
|
Electronic books.
|
| Added Author |
World Scientific (Firm)
|
| ISBN |
9789812833006 (electronic book) |
|
9812833005 (electronic book) |
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