Asymmetric type II periodic motions for nonlinear impact oscillators

作者：Li Yurong; Du Zhengdong^*; Zhang Weinian

来源：Nonlinear Analysis-Theory Methods & Applications, 2008, 68(9): 2681-2696.

DOI：10.1016/j.na.2007.02.015

• impact oscillator
• non-smooth system
• Melnikov method
• subharmonic bifurcation
• Poincare map

In this paper a general class of nonlinear impact oscillators is considered for Type II periodic motions. This system can be used to model an inverted pendulum impacting on rigid walls under external periodic excitation. The unperturbed system possesses a pair of homoclinic cycles and three separate families of periodic orbits inside and outside the homoclinic cycles via the identification given by the impact law. By approximating the Poincare map to O(epsilon) directly, a general method of Melnikov type for detecting the existence of asymmetric Type II subharmonic orbits outside the homoclinic cycles is presented.

• 出版日期2008-5-1
• 单位四川大学; 西南大学