弹簧振子在光滑水平面内的运动规律

2020 , Vol. 39 >Issue 05: 52 - 57

大学生园地

弹簧振子在光滑水平面内的运动规律

展开

徐世浩( 1999—) ，男，山东昌邑人，清华大学机械工程系2017 级本科生.

收稿日期: 2019-07-11

修回日期: 2019-09-10

网络出版日期: 2020-05-17

收起

Spring-mass oscillator confined to horizontal frictionless plain

Expand

1. Department of Mechanical Engineering，Tsinghua University，Beijing 100084，China; 2. School of Aerospace Engineering，Tsinghua University，Beijing 100084，China

Received date: 2019-07-11

Revised date: 2019-09-10

Online published: 2020-05-17

Fold

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.

关键词： 弹簧振子; 双自由度; 非线性运动; 径向运动.

徐世浩, 张雄 . 弹簧振子在光滑水平面内的运动规律[J]. 大学物理, 2020 , 39(05) : 52 -57 . DOI: 10.16854 /j.cnki.1000-0712.190309

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.

Key words： Spring-mass oscillator; two degrees of freedom; nonlinear motion; radial motion

Options

文章导航