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2012 | OriginalPaper | Chapter

Chaos in a Parametrically Excited Pendulum with Damping Force

Author : Chunqing Lu

Published in: Dynamical Systems and Methods

Publisher: Springer New York

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Abstract

The shooting method is applied to prove that a damped pendulum with oscillatory forcing makes chaotic motions for certain parameters. The method is more intuitive than the Poincaré map method and provides more information about when the chaos occurs.

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next chapter Energy and Nonlinear Dynamics of Hybrid Systems
Literature
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Lu C (2006) Chaotic motions of a parametrically exited pendulum. Comm Nonlin Sci Num Sim 11:861–884MATHCrossRef
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Lu C (2007) Choas of a parametrically undamped pendulum. Comm Nonlin Sci Num Sim 12:45–57MATHCrossRef
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Melnikov VK (1963) On the stability of the center for time periodic solutions. Trans Moscow Math Soc (Trudy) 12:3–52
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Wiggins S (1988) On the detection and dynamical consequences of orbits homoclinic to hyperbolic periodic orbits and normally hyperbolic invariant tori in a class of ordinary differential equations. SIAM J Appl Math 48:262–285MathSciNetMATHCrossRef
Metadata
Title
Chaos in a Parametrically Excited Pendulum with Damping Force
Author
Chunqing Lu
Copyright Year
2012
Publisher
Springer New York
Book
Dynamical Systems and Methods

Print ISBN: 978-1-4614-0453-8

Electronic ISBN: 978-1-4614-0454-5

Copyright Year: 2012

DOI
https://doi.org/10.1007/978-1-4614-0454-5_1

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