Resonance And Bifurcation To Chaos In Pendulum - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Resonance And Bifurcation To Chaos In Pendulum write by Albert C J Luo. This book was released on 2017-12-15. Resonance And Bifurcation To Chaos In Pendulum available in PDF, EPUB and Kindle. 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.
The Chaotic Pendulum
The Chaotic Pendulum - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook The Chaotic Pendulum write by M. Gitterman. This book was released on 2010. The Chaotic Pendulum available in PDF, EPUB and Kindle. 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.
The Chaotic Pendulum
The Chaotic Pendulum - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook The Chaotic Pendulum write by Moshe Gitterman. This book was released on 2010-09-07. The Chaotic Pendulum available in PDF, EPUB and Kindle. 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.
Chaos Bifurcations and Fractals Around Us
Chaos Bifurcations and Fractals Around Us - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Chaos Bifurcations and Fractals Around Us write by Wanda Szempli. This book was released on 2003. Chaos Bifurcations and Fractals Around Us available in PDF, EPUB and Kindle. During the last twenty years, a large number of books on nonlinear chaotic dynamics in deterministic dynamical systems have appeared. These academic tomes are intended for graduate students and require a deep knowledge of comprehensive, advanced mathematics. There is a need for a book that is accessible to general readers, a book that makes it possible to get a good deal of knowledge about complex chaotic phenomena in nonlinear oscillators without deep mathematical study.Chaos, Bifurcations and Fractals Around Us: A Brief Introduction fills that gap. It is a very short monograph that, owing to geometric interpretation complete with computer color graphics, makes it easy to understand even very complex advanced concepts of chaotic dynamics. This invaluable publication is also addressed to lecturers in engineering departments who want to include selected nonlinear problems in full time courses on general mechanics, vibrations or physics so as to encourage their students to conduct further study.
Global Transversality, Resonance and Chaotic Dynamics
Global Transversality, Resonance and Chaotic Dynamics - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Global Transversality, Resonance and Chaotic Dynamics write by Albert C. J. Luo. This book was released on 2008. Global Transversality, Resonance and Chaotic Dynamics available in PDF, EPUB and Kindle. This unique book presents a different point of view on the fundamental theory of global transversality, resonance and chaotic dynamics in n-dimensional nonlinear dynamic systems. The methodology and techniques presented in this book are applicable to nonlinear dynamical systems in general. This book provides useful tools for analytical and numerical predictions of chaos in nonlinear Hamiltonian and dissipative systems. All theoretical results are strictly proved. However, the ideas presented in this book are less formal and rigorous in an informal and lively manner. The author hopes the initial ideas may give some inspirations in the field of nonlinear dynamics. With physical concepts, the author also used the simple, mathematical language to write this book. Therefore, this book is very readable, which can be either a textbook for senior undergraduate and graduate students or a reference book for researches in nonlinear dynamics.
