一类共振条件下两个自由度系统的同宿轨道

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基金项目: 国家自然科学基金资助项目(19872044)

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

摘要: 研究一类在参数和强迫激励下发生共振时的两个自由度系统,利用多重尺度法证明存在锁频于Ω的周期解.在一定条件下可变换成Wiggins的系统,给出了判断这类系统同宿轨道存在的计算公式.
- 两个自由度系统 /
- 多重尺度法 /
- 周期解 /
- 同宿轨道 /
- 混沌
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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