| Description |
1 online resource (1 PDF (xiv, 84 pages) :) illustrations (some color) |
| Series |
Synthesis lectures on mechanical engineering, 2573-3176 ; #22 |
|
Synthesis digital library of engineering and computer science.
|
|
Synthesis lectures on mechanical engineering ; #22.
|
| Contents |
1. Introduction -- 2. A semi-analytical method -- 3. Discretization of a parametric pendulum -- 3.1. Implicit discrete mappings -- 3.2. Period-1 motions -- 3.3. Period-m motions |
|
4. Bifurcation trees -- 4.1. Period-1 static points to chaos -- 4.2. Period-1 and period-3 motions to chaos -- 4.3. Independent period-2 motions to chaos -- 4.4. Independent period-4 motions to chaos -- 4.5. Period-5 and period-6 motions to chaos -- 4.6. Independent period-8, period-10, and period-12 motions |
|
5. Harmonic frequency-amplitude characteristics -- 5.1. Discrete fourier series -- 5.2. Non-travelable period-1 static points to chaos -- 5.3. Travelable period-1 motions to chaos -- 5.4. Non-travelable period-2 motions to chaos -- 5.5. Period-3 motions -- 5.6. Period-4 motions |
|
6. Non-travelable periodic motions -- 6.1. Librational periodic motions -- 6.2. Rotational periodic motions |
|
7. Travelable periodic motions -- 7.1. Travelable period-1 to period-4 motions -- 7.2. Travelable period-3 to period-6 motions -- 7.3. Travelable period-5 motions |
| Summary |
The inherent complex dynamics of a parametrically excited pendulum is of great interest in nonlinear dynamics, which can help one better understand the complex world. Even though the parametrically excited pendulum is one of the simplest nonlinear systems, until now, complex motions in such a parametric pendulum cannot be achieved. In this book, the bifurcation dynamics of periodic motions to chaos in a damped, parametrically excited pendulum is discussed. Complete bifurcation trees of periodic motions to chaos in the parametrically excited pendulum include: period-1 motion (static equilibriums) to chaos, and period-m motions to chaos (m = 1,2,···,6,8,···,12). The aforesaid bifurcation trees of periodic motions to chaos coexist in the same parameter ranges, which are very difficult to determine through traditional analysis. Harmonic frequency-amplitude characteristics of such bifurcation trees are also presented to show motion complexity and nonlinearity in such a parametrically excited pendulum system. The non-travelable and travelable periodic motions on the bifurcation trees are discovered. Through the bifurcation trees of travelable and non-travelable periodic motions, the travelable and non-travelable chaos in the parametrically excited pendulum can be achieved. Based on the traditional analysis, one cannot achieve the adequate solutions presented herein for periodic motions to chaos in the parametrically excited pendulum. The results in this book may cause one rethinking how to determine motion complexity in nonlinear dynamical systems |
| Analysis |
parametric pendulum |
|
bifurcation trees to chaos |
|
periodic motions |
|
frequency-amplitude characteristics |
|
non-travelable periodic motion |
|
travelable periodic motions |
| Notes |
Part of: Synthesis digital library of engineering and computer science |
| Bibliography |
Includes bibliographical references (pages 77-82) |
| Notes |
Title from PDF title page (viewed on December 23, 2019) |
| Subject |
Pendulum.
|
|
Bifurcation theory.
|
|
Bifurcation theory
|
|
Pendulum
|
| Form |
Electronic book
|
| Author |
Luo, Albert C. J., author
|
| ISBN |
1681736853 |
|
9781681736853 |
|
9783031796456 |
|
3031796454 |
|
