秋千参数自激振动的数学模型与数值模拟  

The mathematic model and numerical simulation of swing with parametric self-excited oscillation

作　　者：杨百愚[1] 王翠香 王斌科[1] 李春旺[1] 范琦 田昌会[1] YANG Bai-yu;WANG Cui-xiang;WANG Bin-ke;LI Chun-wang;FAN Qi;TIAN Chang-hui(Department of Basic Sciences,Air Force Engineering University,Xi'an,Shaanxi,710051,China)

机构地区：[1]空军工程大学基础部

出　　处：《大学物理》2020年第1期53-56,共4页College Physics

基　　金：国家自然科学基金项目(51575524)资助

摘　　要：将秋千视为变长度单摆,基于归一化高斯函数构造了摆球相对摆杆的速度表达式.在此基础上建立了秋千的非线性动力学微分方程,并据此数学模型对秋千运动进行了数值模拟,得到了秋千的运动规律和功能转化的机制.The swing is regarded as a variable length simple pendulum.Based on the normalized Gauss function,the velocity of pendulum ball relative to pendulum rod is designed.On this basis,the nonlinear dynamic differential equation of swing is established,and the motion of swing is simulated numerically based on this mathematic model,the motion,work and energy transformation mechanism of swing are obtained.

关 键 词：秋千 参数自激振动 数学模型 数值模拟 

分 类 号：O323[理学—一般力学与力学基础]