拉格朗日陀螺转动的有效势能和可视化  

Effective potential energy and visualization of rotation of Lagrangian gyro

作　　者：周群益 周丽丽[2] 莫云飞 侯兆阳 ZHOU Qun-yi;ZHOU Li-li;MO Yun-fei;HOU Zhao-yang(College of General Education,Guangzhou Institute of Science and Technology,Guangzhou,Guangdong 510540,China;School of Medical and Information Engineering,Gannan Medical University,Ganzhou,Jiangxi 341000,China;School of Electronic Information and Electrical Engineering,Changsha University,Changsha,Hunan 410022,China;School of Science,Chang an University,Xi an,Shaanxi 710064,China)

机构地区：[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

出　　处：《大学物理》2021年第9期13-20,27,共9页College Physics

基　　金：广东省高校科研特色创新项目(2020KTSCX209);国家自科基金(12004053)资助。

摘　　要：对《对称陀螺在重力场中定点转动的分析》一文中的能量守恒公式提出质疑,并推导证明了正确的公式.在有效势能的公式中引入了两个守恒参数,求出了有效势能的导数和二阶导数,并且求出了导数为零时的有效势能和二阶导数,通过作图和分析,说明了陀螺转动中章动角的变化范围和在平衡点的稳定性.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.

关 键 词：拉格朗日陀螺 有效势能 章动角 稳定性 

分 类 号：O313.3[理学—一般力学与力学基础]