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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

  • Wang Mao-nan
  • Xu Zhen-yuan
Article
  • 28 Downloads

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.

Key words

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

CLC number

O175.14 

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References

  1. [1]
    Nayfeh A H, Mook D T.Nonlinear Oscillations [M]. New York: John Wiley & Sons, 1979.Google Scholar
  2. [2]
    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
  3. [3]
    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.MathSciNetGoogle Scholar

Copyright information

© Editorial Committee of Applied Mathematics and Mechanics 1980

Authors and Affiliations

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

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