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


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].


Mathematical Modeling Periodic Solution Industrial Mathematic Chaotic Behavior Parameter Region 
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Copyright information

© Shanghai University of Technology (SUT) 1988

Authors and Affiliations

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

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