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Applied Mathematics and Mechanics

, Volume 22, Issue 3, pp 340–352 | Cite as

On the Homoclinic Orbits in a Class of Two-Degree-of-Freedom Systems under the Resonance Conditions

  • Mao-nan Wang
  • Zhen-yuan Xu
Article

Abstract

A class of two-degree-of-freedom systems in resonance with an external, parametric excitation is investigated, the existence of the periodic solutions locked to Ω is proved by the use of the method of multiple scales. This systems can be transformed into the systems of Wiggins under some conditions. A calculating formula which determines the existence of homoclinic orbits of the systems is given.

a two-degree-of-freedom system method of multiple scales periodic solution homoclinic orbit chaos 

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References

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    Nayfeh A H, Mook D T. Nonlinear Oscillations[M]. New York: John Wiley & Sons,1979.Google Scholar
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    FENG Zai-chun, Wiggins S. On the existence of chaos in a class of two-degree-of-freedom, damped, strongly parametrically forced mechanical systems with broken O(2) symmetry [J]. Z Angew Mach Phys, 1993,44(2):200–248.Google Scholar
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    Kovačič G, Wiggins S. Orbits homoclinic to resonances, with an application to chaos in a model of the forced and damped sine-Gordon equation[J]. Physica D,1992,57(1–2):185–225.Google Scholar

Copyright information

© Kluwer Academic Publishers 2001

Authors and Affiliations

  • Mao-nan Wang
    • 1
  • Zhen-yuan Xu
    • 1
  1. 1.Mathematics and Physics InstituteWuxi University of Light IndustryWuxiP R China

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