• 教学讨论 •

### 拉格朗日陀螺转动的有效势能和可视化

1. 1. 广州理工学院通识教育学院，广东广州 510540;2. 赣南医学院医院信息工程学院，江西赣州 341000; 3. 长沙学院电子信息与电气工程学院，湖南长沙 410022;4. 长安大学理学院应用物理系，陕西西安 710064
• 收稿日期:2021-01-25 修回日期:2021-05-06 出版日期:2021-09-20 发布日期:2021-09-24
• 通讯作者: 莫云飞，E-mail：moyunfei8899@ ccsu.edu.cn
• 作者简介:周群益(1955—)，男，湖南衡阳人，广州理工学院副教授，主要从事凝聚态物理研究.
• 基金资助:
广东省高校科研特色创新项目(2020KTSCX209);国家自科基金(12004053)资助

### Effective potential energy and visualization of rotation of Lagrangian gyro

ZHOU Qun-yi1，ZHOU Li-li2，MO Yun-fei3，HOU Zhao-yang4

1. 1. College of General Education，Guangzhou Institute of Science and Technology，Guangzhou，Guangdong 510540，China; 2. School of Medical and Information Engineering，Gannan Medical University，Ganzhou，Jiangxi 341000，China; 3. School of Electronic Information and Electrical Engineering，Changsha University，Changsha，Hunan 410022，China; 4. School of Science，Chang'an University，Xi'an，Shaanxi 710064，China

Abstract: In this paper，the energy conservation formula in the article “Analysis of the rotation modes of the

symmetric top around fixed point in gravitational field”has been questioned，and the correct formula has been deduced

and proved. Two conservation parameters are introduced in the formula of effective potential energy，and the

derivative and the second derivative of the effective potential energy are obtained. In addition，the effective potential

energy and second-order derivative have also been calculated when the derivative is zero. Through drawing and analysis，

the range of the change of nutation angle during the gyro rotation and the stability at the equilibrium point

are explained.