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Applied Mathematics and Mechanics

, Volume 9, Issue 12, pp 1195–1204 | Cite as

Periodic solution and chaotic behavior of a class of nonautonomic pendulum systems with large damping

  • Sun Jian-hua
Article
  • 20 Downloads

Abstract

In this paper the existence and uniqueness of the periodic solution is studied for a class of second order nonautonomic pendulum systems
$$\bar x + a\dot x + \varphi (t)\sin x = F(t)$$
and the parameter regions for which the system in chaos is investigated when
$$\varphi (t) = 1 - \varepsilon \lambda \cos \omega t, F(t) = \beta + \varepsilon \mu (\cos \omega t - \omega \sin \omega t)$$
and the damping coefficient a>0 is large. The results obtained generalize the corresponding conclusions of papers [1–8].

Keywords

Mathematical Modeling Periodic Solution Industrial Mathematic Chaotic Behavior Parameter Region 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

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    Sun Jian-hua, Chaotic motions of the pendulum systems.J. Nanjing University, Math. Biquarterly,4, 1 (1987), 43–50. (in chinese)Google Scholar
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    Lasalle, J.I., and S. Lefschetz,Stability by Lyapunov's Direct Method with Application. New York, Academic Press (1961).Google Scholar

Copyright information

© Shanghai University of Technology (SUT) 1988

Authors and Affiliations

  • Sun Jian-hua
    • 1
  1. 1.Nanjing UniversityNanjing

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