Rotating orbits of a parametrically-excited pendulum

X. Xu, M. Wiercigroch, M.P. Cartmell

Research output: Contribution to journalArticle

97 Citations (Scopus)

Abstract

The authors consider the dynamics of the harmonically excited parametric pendulum when it exhibits rotational orbits. Assuming no damping and small angle oscillations, this system can be simplified to the Mathieu equation in which stability is important in investigating the rotational behaviour. Analytical and numerical analysis techniques are employed to explore the dynamic responses to different parameters and initial conditions. Particularly, the parameter space, bifurcation diagram, basin of attraction and time history are used to explore the stability of the rotational orbits. A series of resonance tongues are distributed along the non-dimensionalied frequency axis in the parameter space plots. Different kinds of rotations, together with oscillations and chaos, are found to be located in regions within the resonance tongues.
LanguageEnglish
Pages1537-1548
Number of pages12
JournalChaos, Solitons and Fractals
Volume23
Issue number5
DOIs
Publication statusPublished - 31 Mar 2005

Fingerprint

Pendulum
Parameter Space
Rotating
Orbit
Oscillation
Mathieu Equation
Basin of Attraction
Bifurcation Diagram
Dynamic Response
Numerical Analysis
Damping
Chaos
Initial conditions
Angle
Series
History

Keywords

  • pendulum
  • rotational orbits
  • Mathieu equation

Cite this

Xu, X. ; Wiercigroch, M. ; Cartmell, M.P. / Rotating orbits of a parametrically-excited pendulum. In: Chaos, Solitons and Fractals. 2005 ; Vol. 23, No. 5. pp. 1537-1548.
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Rotating orbits of a parametrically-excited pendulum. / Xu, X.; Wiercigroch, M.; Cartmell, M.P.

In: Chaos, Solitons and Fractals, Vol. 23, No. 5, 31.03.2005, p. 1537-1548.

Research output: Contribution to journalArticle

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