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

WANG Mao-nan; XU Zhen-yuan

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WANG Mao-nan, XU Zhen-yuan. On the Homoclinic Orbits in a Class of Two-Degree of Freedom Systems Under the Resonance Conditions[J]. Applied Mathematics and Mechanics, 2001, 22(3): 295-306.

Citation:

WANG Mao-nan, XU Zhen-yuan. On the Homoclinic Orbits in a Class of Two-Degree of Freedom Systems Under the Resonance Conditions[J]. Applied Mathematics and Mechanics, 2001, 22(3): 295-306.

Citation:

WANG Mao-nan, XU Zhen-yuan. On the Homoclinic Orbits in a Class of Two-Degree of Freedom Systems Under the Resonance Conditions[J]. Applied Mathematics and Mechanics, 2001, 22(3): 295-306.

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

Mathematics and Physics Institute, Wuxi University of Light Industry, Wuxi 214036, P R China

Received Date: 2000-05-08
Rev Recd Date: 2000-10-29
Publish Date: 2001-03-15

Abstract

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 8 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 exsitence 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(3)

References

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[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.
[3]	Kovacic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.