The Parametrically Excited Pendulum and the Criteria for Predicting the Onset of Chaos PDF Download

Author: Tseng-Hsing Hsu
Publisher:
ISBN:
Category : Chaotic behavior in systems
Languages : en
Pages : 122

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Book Description

Author: Albert C J Luo
Publisher: World Scientific
ISBN: 9813231696
Category : Science
Languages : en
Pages : 251

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Book Description
A periodically forced mathematical pendulum is one of the typical and popular nonlinear oscillators that possess complex and rich dynamical behaviors. Although the pendulum is one of the simplest nonlinear oscillators, yet, until now, we are still not able to undertake a systematical study of periodic motions to chaos in such a simplest system due to lack of suitable mathematical methods and computational tools. To understand periodic motions and chaos in the periodically forced pendulum, the perturbation method has been adopted. One could use the Taylor series to expend the sinusoidal function to the polynomial nonlinear terms, followed by traditional perturbation methods to obtain the periodic motions of the approximated differential system.This book discusses Hamiltonian chaos and periodic motions to chaos in pendulums. This book first detects and discovers chaos in resonant layers and bifurcation trees of periodic motions to chaos in pendulum in the comprehensive fashion, which is a base to understand the behaviors of nonlinear dynamical systems, as a results of Hamiltonian chaos in the resonant layers and bifurcation trees of periodic motions to chaos. The bifurcation trees of travelable and non-travelable periodic motions to chaos will be presented through the periodically forced pendulum.

Author: Moshe Gitterman
Publisher: World Scientific
ISBN: 9814464244
Category : Science
Languages : en
Pages : 157

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Book Description
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.

Author: M. Gitterman
Publisher: World Scientific
ISBN: 9814322008
Category : Science
Languages : en
Pages : 157

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Book Description
The chaotic behavior of pendulum is usually associated with the random force acting on a pendulum (Brownian motion). 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.

Author:
Publisher:
ISBN:
Category : Mechanics, Applied
Languages : en
Pages : 338

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Book Description

Author: Jon Juel Thomsen
Publisher: Springer Nature
ISBN: 3030680452
Category : Technology & Engineering
Languages : en
Pages : 539

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Book Description
An ideal text for students that ties together classical and modern topics of advanced vibration analysis in an interesting and lucid manner. It provides students with a background in elementary vibrations with the tools necessary for understanding and analyzing more complex dynamical phenomena that can be encountered in engineering and scientific practice. It progresses steadily from linear vibration theory over various levels of nonlinearity to bifurcation analysis, global dynamics and chaotic vibrations. It trains the student to analyze simple models, recognize nonlinear phenomena and work with advanced tools such as perturbation analysis and bifurcation analysis. Explaining theory in terms of relevant examples from real systems, this book is user-friendly and meets the increasing interest in non-linear dynamics in mechanical/structural engineering and applied mathematics and physics. This edition includes a new chapter on the useful effects of fast vibrations and many new exercise problems.

Author: A.A. Tsonis
Publisher: Springer Science & Business Media
ISBN: 1461533600
Category : Science
Languages : en
Pages : 279

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Book Description
Based on chaos theory two very important points are clear: (I) random looking aperiodic behavior may be the product of determinism, and (2) nonlinear problems should be treated as nonlinear problems and not as simplified linear problems. The theoretical aspects ofchaos have been presented in great detail in several excellent books published in the last five years or so. However, while the problems associated with applications of the theory-such as dimension and Lyapunov exponentsestimation, chaosand nonlinear pre diction, and noise reduction-have been discussed in workshops and ar ticles, they have not been presented in book form. This book has been prepared to fill this gap between theory and ap plicationsand to assist studentsand scientists wishingto apply ideas from the theory ofnonlinear dynamical systems to problems from their areas of interest. The book is intended to be used as a text for an upper-level undergraduate or graduate-level course, as well as a reference source for researchers. My philosophy behind writing this book was to keep it simple and informative without compromising accuracy. I have made an effort to presentthe conceptsby usingsimplesystemsand step-by-stepderivations. Anyone with an understanding ofbasic differential equations and matrix theory should follow the text without difficulty. The book was designed to be self-contained. When applicable, examples accompany the theory. The reader will notice, however, that in the later chapters specific examples become less frequent. This is purposely done in the hope that individuals will draw on their own ideas and research projects for examples.

Author:
Publisher:
ISBN:
Category : Shock (Mechanics)
Languages : en
Pages : 568

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Book Description

Author: Steven H. Strogatz
Publisher: CRC Press
ISBN: 0429961111
Category : Mathematics
Languages : en
Pages : 532

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Book Description
This textbook is aimed at newcomers to nonlinear dynamics and chaos, especially students taking a first course in the subject. The presentation stresses analytical methods, concrete examples, and geometric intuition. The theory is developed systematically, starting with first-order differential equations and their bifurcations, followed by phase plane analysis, limit cycles and their bifurcations, and culminating with the Lorenz equations, chaos, iterated maps, period doubling, renormalization, fractals, and strange attractors.

Author: Gen Matsumoto
Publisher: World Scientific
ISBN: 9814544353
Category :
Languages : en
Pages : 1119

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Book Description
Soft computing is the common name for a certain form of natural information processing that has its original form in biology, especially in the function of human brain. It is a discipline rooted in a group of technologies such as fuzzy logic, neural networks, chaos, genetic algorithms, probabilistic reasoning and learning algorithms. Today, soft computing has become an acknowledged concept; however, for a long time, such components of soft computing have been debated and individually developed.Since its beginning in 1990, the series of IIZUKA conferences has covered various kinds of technologies that constitute soft computing. This series has played a pioneering role in promoting the development of a symbiotic relationship between the various technologies of soft computing.At IIZUKA'98, the 5th International Conference on Soft Computing and Information/Intelligent Systems, new developments and results in this field were introduced and discussed by researchers from academic, governmental and industrial institutions around the world.This volume presents the opening lecture by Prof. Walter J Freeman, the keynote speech by Dr Gen Matsumoto, the plenary lectures by 5 eminent researchers and about 230 carefully selected papers drawn from more than 25 countries. It documents current research and in-depth studies on the fundamental aspects of soft computing and their practical applications.