一类共振条件下两个自由度系统的同宿轨道

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

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 。

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 exsitence of homoclinic orbits of the systems is given.