拉格朗日陀螺转动的有效势能和可视化

doi:10.16854 / j.cnki.1000- 0712.210078

College Physics ›› 2021, Vol. 40 ›› Issue (9): 13-.doi: 10.16854 / j.cnki.1000- 0712.210078

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Effective potential energy and visualization of rotation of Lagrangian gyro

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

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

Received:2021-01-25 Revised:2021-05-06 Online:2021-09-20 Published:2021-09-24

Abstract

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.

Key words: Lagrangian gyro, effective potential energy, nutation angle, stability

ZHOU Qun-yi, ZHOU Li-li, MO Yun-fei, HOU Zhao-yang. Effective potential energy and visualization of rotation of Lagrangian gyro[J].College Physics, 2021, 40(9): 13-.

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Effective potential energy and visualization of rotation of Lagrangian gyro

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