摘要
以不受阻力作用的均质细杆作为复摆的物理模型进行复摆周期的研究.应用数学软件Mathematica,首先对任意摆角以椭圆积分表示的周期以及由该公式得到的近似表示到sin6(θ20)高阶项的周期计算.通过比较两者的周期,验证了近似解析式表示周期的适用的摆角范围在0°≤θ0≤40°,其次从复摆摆动的非线性微分方程出发,数值研究在几种因素影响下的复摆周期,得到一些有意义的结果.在我们的研究中特别对复摆的"小角度"作出了较好的限定.
In this paper,we investigated periods of the compound pendulum for the physical model of homogeneous thin rod without any resistance during oscillating movements.Firstly,based on Mathematica software,we calculated the period with two different methods,namely,normal elliptic integral and sixth-order approximated elliptic integrals.By comparing them,it was confirmed that the sixth-order approximated method is only suited for the oscillation angle in the range 0°≤θ0≤40°.Secondly,the effects of several factors on the period of the compound pendulum were investigated by numerical approach from nonlinear differential equation,and the meaningful results were obtained.Especially,＂the small angle＂ was a preferable constrained in our studies.
出处
《重庆文理学院学报（自然科学版）》
2011年第6期30-35,共6页
Journal of Chongqing University of Arts and Sciences
