中文摘要：

将Melnikov方法应用于碰振准哈密顿系统的局部亚谐轨道,推导出了局部亚谐轨道的Melnikov函数。该函数可以用于确定存在局部亚谐轨道及极限环分岔的条件。给出的局部亚谐轨道Melnikov函数和同宿轨道Melnikov函数共同揭示了准哈密顿系统的诸多动力学特征;然后,通过数值方法模拟受迫碰振振子运动,验证了局部亚谐Melnikov函数的正确性。

英文摘要：

The Melnikovfs method is applied on a vibro-impact quasi-Hamiltonian system, and a Melnikov function for local- subharmonic orbits is derived. The function can be applied to determine the existence of local-subharmonic orbits, as well as the conditions of limit cycle bifurcations. The so-called local subharmonic Melnikov function, together with the one for homoclinic orbit, reveals lots of dynamical features of the quasi-Hamiltonian system. The local-subharmonic Melnikov function is validated by numerical simulations of a forced vibro-impact oscillator.