Resonance and Bifurcation to Chaos in Pendulum

Nonfiction, Science & Nature, Science, Physics, Dynamics, Chaotic Behavior, Mathematics
Cover of the book Resonance and Bifurcation to Chaos in Pendulum by Albert C J Luo, World Scientific Publishing Company
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Author: Albert C J Luo ISBN: 9789813231696
Publisher: World Scientific Publishing Company Publication: December 15, 2017
Imprint: WSPC/HEP Language: English
Author: Albert C J Luo
ISBN: 9789813231696
Publisher: World Scientific Publishing Company
Publication: December 15, 2017
Imprint: WSPC/HEP
Language: English

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.

Contents:

  • Resonance and Hamiltonian Chaos
  • Hamiltonian Chaos in Pendulum
  • Parametric Chaos in Pendulum
  • Nonlinear Discrete Systems
  • Periodic Flows in Continuous Systems
  • Periodic Motions to Chaos in Pendulum

Readership: Researchers and academics in the field of mathematics.
0

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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.

Contents:

Readership: Researchers and academics in the field of mathematics.
0

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