摘要
以相图和庞加莱点作为表征手段,本文对受外力驱动的一种非线性动力学系统混沌摆的摆动行为进行研究,考察了该混沌摆系统的运动状态随驱动力频率变化的特征。同时我们建立了该系统的理论模型,通过数值计算模拟该混沌摆运动状态来验证实验结果。实验和仿真结果均表明,随着驱动力频率的增加,混沌摆会有周期和混沌运动状态交替出现的情况,且这种变化近乎为突变的。同时,也从数值仿真结果中观察到了混沌摆运动状态对驱动力频率这一参数的敏感性。本文阐述的仿真和测量研究可以作为本科生的大学物理实验课程中混沌摆实验项目的拓展内容,使有兴趣和能力的同学对非线性动力学系统的混沌现象有更深入的理解和认识。
A kind of nonlinear dynamical system,chaotic pendulum is established and chaos phenomenon driven by periodic force can be demonstrated.The phase diagram and Poincare point are used as the means of characterization to study dynamical character the chaotic pendulum.Changing the driving force frequency of the chaotic pendulum instrument,the system can demonstrate different nonlinear dynamic behaviors.And at the same time,we establish a theory mode to describe the chaotic pendulum.The numerical simulation results agree well with the experiment results.With the increase of the driving frequency,the chaotic pendulum will appear alternately in the periodic and chaotic states,and this change is almost abrupt.At the same time,the sensitivity of the chaotic pendulum motion state to the driving force frequency is also observed from the numerical simulation results.
作者
李明达
董乔南
杨亚利
李鑫
罗锻斌
LI Mingda;DONG Qiaonan;YANG Yali;LI Xin;LUO Duanbin(Department of Physics, East China University of Science and Technology, Shanghai 200237)
出处
《物理与工程》
2019年第6期77-84,88,共9页
Physics and Engineering
基金
华东理工大学2018年度实验实践教学改革与建设立项(BK0121004)
华东理工大学2019年本科教育教学方法改革“突出传感技术应用的物理实验课程教学体系建设”研究项目资助
关键词
混沌摆
驱动频率
相图
转动传感器
数值模拟
chaotic pendulum
driving frequency
phase diagram
motion sensors
numerical simulation
