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Existence of quasi-periodic solutions of the real pendulum equation

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  • Lu, Lin
  • Li, Xuemei

Abstract

The pendulum equation x¨=-αx-δẋ-(1+f0cosω1t)sinx+f1sinω2t is considered in this paper, where f0,f1 and δ are small real parameters, the ratio of ω1 and ω2 is irrational, and frequencies ω1 and ω2 satisfy the Diophantine condition. The unperturbed system (f0=f1=δ=0) has several fixed points for different parameter α. We use KAM theory to prove that the perturbed system possesses quasi-periodic solutions in neighborhoods of those fixed points.

Suggested Citation

  • Lu, Lin & Li, Xuemei, 2014. "Existence of quasi-periodic solutions of the real pendulum equation," Chaos, Solitons & Fractals, Elsevier, vol. 62, pages 23-33.
    • Handle: RePEc:eee:chsofr:v:62-63:y:2014:i::p:23-33
    DOI: 10.1016/j.chaos.2014.03.003
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