ON THE HOMOCLINIC ORBITS IN A CLASS OF TWO-DEGREE-OF-FREEDOM SYSTEMS UNDER THE RESONANCE CONDITIONS

Applied Mathematics and Mechanics (English Edition) ›› 2001, Vol. 22 ›› Issue (3): 340-352.

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ON THE HOMOCLINIC ORBITS IN A CLASS OF TWO-DEGREE-OF-FREEDOM SYSTEMS UNDER THE RESONANCE CONDITIONS

WANG Mao-nan, XU Zhen-yuan

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

Received:2000-05-08 Revised:2000-10-29 Online:2001-03-18 Published:2001-03-18
Supported by:
the National Natural Science Foundation of China(19872044)

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 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

2010 MSC Number:

O175.14

WANG Mao-nan;XU Zhen-yuan. ON THE HOMOCLINIC ORBITS IN A CLASS OF TWO-DEGREE-OF-FREEDOM SYSTEMS UNDER THE RESONANCE CONDITIONS. Applied Mathematics and Mechanics (English Edition), 2001, 22(3): 340-352.

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ON THE HOMOCLINIC ORBITS IN A CLASS OF TWO-DEGREE-OF-FREEDOM SYSTEMS UNDER THE RESONANCE CONDITIONS

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