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| 用Mathematica软件对无阻力复摆周期的研究 | |
| 引用本文： | 程光明,石代蓉,陈希明. 用Mathematica软件对无阻力复摆周期的研究[J]. 重庆文理学院学报(自然科学版), 2011, 30(6): 30-35 |
| 作者姓名： | 程光明 石代蓉 陈希明 |
| 作者单位： | 1. 重庆市渝北区教师进修学校,重庆渝北,401120 2. 第三军医大学西南医院,重庆沙坪坝,400038 3. 重庆邮电大学数理学院,重庆南岸,400065 |
| 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... |
| 关 键 词： | MATHEMATICA 复摆 周期 |
Investigation of period without any resistance for the compound pendulum by Mathematica |
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| Abstract: | 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. |
| Keywords: | Mathematica compound pendulum period |
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