文献类型：期刊文献

中文题名：弹簧车摆的动力学模拟研究

英文题名：SIMULATION STUDY ON THE DYNAMICS OF SPRING CAR PENDULUM

作者：刘锦[1];张孟[1]

机构：[1]华东理工大学物理学院,上海200237

年份：2021

卷号：31

期号：5

起止页码：93

中文期刊名：物理与工程

外文期刊名：Physics and Engineering

收录：CSTPCD

基金：2019年华东理工大学教改项目(80222301901001);2020年华东理工大学教师思政和师德建设研究课题(重点项目)(YK0109002)资助。

语种：中文

中文关键词：弹簧车摆;非线性系统;数值模拟;物理教学

外文关键词：spring car pendulum;nonlinear systems;numerical simulation;physics teaching

摘要：弹簧牵引下的车摆模型是一个复杂的不可积非线性动力学体系,采用牛顿力学定律建立了车摆模型的动力学方程,运用Matlab软件进行计算机数值模拟并详细讨论了车摆模型中小球和车随时间动力学演化过程和运动特征。研究发现摆球的运动在多数情况下是混沌的,同时也会出现拟周期运动,并在一定范围内出现混沌和拟周期运动并存且交替变化的阵发性混沌运动现象。直观描绘出摆球运动中轨迹图、相图、时域图对下落角度初始值的极端敏感依赖性。通过数值模拟处理不可积系统得到的计算结果为车摆相关模型的物理教学和研究提供参考依据。
The car pendulum model under spring traction is a complex integrable nonlinear dynamical system.The dynamic equation of the car pendulum model is established by Newton's law of mechanics.The computer numerical simulation is carried out by using Matlab software.The dynamic evolution process and motion characteristics of the ball and car with time in the car pendulum model are discussed in detail.It is found that the motion of the pendulum ball is chaotic in most cases,and quasi-periodic motion also appears.In a certain range,there is a paroxysmal chaotic motion in which chaos and quasi-periodic motion coexist and change alternately.The extremely sensitive dependence of trajectory,phase,and time-domain diagrams on the initial value of the falling angle in the pendulum motion is depicted intuitively.The results obtained by numerical simulation of non-integrable systems can provide a reference for the physics teaching and research of car pendulum related models.