摘要
在非线性双自由度运动的弹簧振子中,光滑水平面内运动的模型具有运动微分方程简单、变量可分离的特点.本文通过极坐标描述法,建立了弹簧振子在光滑水平面内的运动微分方程.将与径向运动有关的变量分离出来,建立了径向运动微分方程,并基于其非线性的特点进行了定性分析和近似求解.使用MATLAB数值求解,模拟弹簧振子的运动轨迹,验证了本文的定性分析结论和两种特殊情形下的近似解的精度.
Among spring-mass oscillators with nonlinear motions and two degrees of freedom, the model confined to horizontal frictionless plane has features of simple dynamic differential equations and separable variables. In this study polar coordinates are used to construct the dynamic differential equations of the spring-mass oscillator confined to horizontal frictionless plain. Variables related to radial motion are separated to form an individual dynamic differential equation, which is researched by qualitative analysis and approximation theory due to its nonlinear characteristic. Software MATLAB is used as a numerical method to simulate paths of the oscillator, verify qualitative results and demonstrate the accuracy of approximate solutions in two specific situations.
作者
徐世浩
张雄
XU Shi-hao;ZHANG Xiong(Department of Mechanical Engineering,Tsinghua University,Beijing 100084,China;School of Aerospace Engineering,Tsinghua University,Beijing 100084,China)
出处
《大学物理》
2020年第5期52-57,69,共7页
College Physics
关键词
弹簧振子
双自由度
非线性运动
径向运动
Spring-mass oscillator
two degrees of freedom
nonlinear motion
radial motion
