倒摆运动的混沌行为  

The chaos character of the movement of inverse pendulum

作　　者：陈立宏[1] 彭建华[1] 夏彬[1] 王广[1] 高东明 

机构地区：[1]东北师范大学物理学院,吉林长春130024 [2]秦皇岛市一中,河北秦皇岛066000

出　　处：《大学物理》2005年第9期44-47,共4页College Physics

摘　　要：设计一个受周期外力驱动的倒摆实验装置,并建立该系统的动力学方程,用线性稳定性分析方法讨论了平衡点附近邻域的稳定性,利用数值计算并结合多种分析方法求解非线性方程并判断解的性质.通过改变系统参数,画出时域图、相图及分岔图,计算分析和实验发现,这个简单的力学系统存在十分丰富的动力学行为(分岔、混沌).理论分析、数值模拟和实验结果一致.An experimental device of the forced inverse pendulum is designed and the dynamical equation is proposed. By using the method of the linear stability analysis, the stability of the system is discussed in the neighborhood of the equilibrium points. The character of the solutions can be obtained by numerical simulation and other analysis methods. From the results of computer simulation and experiment some time-series diagrams, phase diagrams and bifurcation diagrams for the oscillations of this system, these show that there are various kind of dynamical phenomena in this simple system. Theory analysis and numerical simulation well agree with the experiment results.

关 键 词：倒摆 线性稳定性 平衡点 分岔 混沌 

分 类 号：O415.5[理学—理论物理] O32[理学—物理]