基于Matlab GUI受不稳定约束弹簧振子运动的研究
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摘要
利用拉格朗日方程推导出在水平面上受不稳定约束弹簧振子运动的动力学方程,运用Matlab软件对动力学方程进行数值求解,并通过Matlab图形用户界面(Graphical User Interface,GUI)对不同条件下弹簧振子运动进行仿真,绘制了弹簧振子坐标随时间变化的演化曲线、相图以及运动轨迹,得到了更为直观的弹簧振子运动规律。结果表明,弹簧振子运动与弹簧一端的运动速度大小和初始角度有关;在一定条件下,弹簧振子作准周期运动。
Based on Lagrange equation,the kinetic equation about an unstable constraint spring oscillator on a horizontal plane is derived. The dynamic equation is solved numerically with Matlab software,and the spring oscillator motion under different conditions is simulated with Matlab Graphical User Interface( GUI). A more intuitive law of the spring oscillator motion is obtained by drawing the evolution curve,phase diagram and motion trajectory. The results indicate that the spring oscillator motion is related to the speed at the end-point and initial angle of the spring,and the spring oscillator motion is quasi-periodic under certain conditions.
Based on Lagrange equation,the kinetic equation about an unstable constraint spring oscillator on a horizontal plane is derived. The dynamic equation is solved numerically with Matlab software,and the spring oscillator motion under different conditions is simulated with Matlab Graphical User Interface( GUI). A more intuitive law of the spring oscillator motion is obtained by drawing the evolution curve,phase diagram and motion trajectory. The results indicate that the spring oscillator motion is related to the speed at the end-point and initial angle of the spring,and the spring oscillator motion is quasi-periodic under certain conditions.
引文
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[2]赵凯华,罗蔚茵.新概念物理教程·力学[M].北京:高等教育出版社,2001.
[3]杨正波,夏清华,刘思平.不同控制参数下的弹簧摆[J].大学物理,2011,30(5):23-26.
[4]夏清华,屈少华.受不稳定约束弹簧摆运动的研究[J].大学物理,2015,34(4):6-10.
[5]李硕,赵彤帆,李根全,等.Matlab软件在单摆自由振动中的应用[J].实验室研究与探索,2013,32(11):65-68.
[6]李阳,王宏,韩艳玲.与r的一次方成正比有心力作用下质点的运动研究[J].物理通报,2015,34(12):4-8.
[7]李阳,王宏,韩艳玲,等.在水平面上受稳定约束的弹簧振子运动研究[J].广西物理,2015,36(2):31-34.
[8]黄焱.双弹簧振子在竖直方向的自由振动研究[J].大学物理,2014,33(9):20-23.
[9]何松林,黄焱,戴祖诚.对称双弹簧振子横向振动的复杂性研究[J].昆明学院学报,2010,32(3):86-88.
[10]杨正波,夏清华,刘思平.多弹簧振子耦合系统运动研究[J].大学物理,2010,29(4):29-32.
[11]钟可君,张海林.基于Matlab GUI设计的光学实验仿真[J].实验室研究与探索,2010,29(10):52-53.
[12]朱飞宇,徐志宇,黄国辉,等.基于Matlab GUI的三容水箱液位实时监控系统设计[J].实验室研究与探索,2017,36(9):83-86.
[13]温正.MATLAB科学计算[M].北京:清华大学出版社,2017.
[14]罗华飞.MATLAB GUI设计学习手记[M].3版.北京:北京航空航天大学出版社,2014.
[15]Hunt B R,Lipsman R L,Rosenberg J M.A guide to MATLAB:for beginners and experienced users[M].Cambridge:Cambridge University Press,2014.
[16]Zhang Z,Bai H,Yang G,et al.Computer simulation of Fraunhofer diffraction based on MATLAB[J].Optik-International Journal for Light and Electron Optics,2013,124(20):4449-4451.