SHI Yurong;WANG Guangxing;ZHONG Yiyang;GU Yongjian;

• 1:College of Physics and Optoelectronic Engineering
• 2:Ocean university of China
• 3:Department of Quantum Science and Technology
• 4:The Australian National University

Abstract：

The counterintuitive phenomenon of precession and nutation of gyroscopes in the gravitational field is surprising, but qualitative explanations using Cartesian coordinate systems can only explain precession but not nutation, and cannot provide satisfactory answers for students in the general physics and mechanics stage. This paper derives the form of the angular momentum theorem in spherical coordinates and applies it to the dynamic analysis of the precession and nutation of gyroscopes. With the help of numerical simulation methods, several relationship diagrams of the gyroscope's motion quantities are given, providing students with clear dynamic images and allowing ordinary physics students to understand the complex motion of gyroscopes. This analysis method is simpler, more intuitive, and easier to understand than the Lagrangian mechanics method of theoretical mechanics.

Key Words： spherical coordinates;gyroscope;precession;nutation;movement analysis

Abstract:

Keywords:

Foundation: 中国海洋大学本科教育教学研究重点项目：理实并重、与时创新、因材施教理念下的“力学”课程建设（2024ZD08）

Authors: SHI Yurong;WANG Guangxing;ZHONG Yiyang;GU Yongjian;

References：

• [1]廖耀发,佘守宪.陀螺与陀螺仪进动及章动的一种初等分析[J].湖北工业学院学报,2004,(5):43-46.LIAO Y F, SHE S X. An elementary analysis of precession and nutation of top and gyrascope[J]. Journal of Hubei University of Technology, 2004,(5):43-46.(in Chinese)
• [2]常振军,张志利,周召发.陀螺仪进动与章动运动分析[J].传感器与微系统,2012(9):54-56.CHANG Z J, ZHANG Z L, ZHOU Z F. Movement analysis of precession and nutation of gyroscope[J].Transducer and Microsystem Technologies, 2012(9):54-56.(in Chinese)
• [3]施鹏毅,涂展春.对球坐标系质点加速度的理解与严格推导[J].大学物理,2020,39(7):60-62,65.SHI P Y, TU Z C. The intuitive understanding and strict derivation of particle acceleration in spherical coordinate system[J]. College Physics, 2020, 39(7):60-62, 65.(in Chinese)
• [4]赵凯华,罗蔚茵.力学[M].2版.北京:高等教育出版社.2004:195-196.ZHAO K H, LUO Y Y. Mechanics[M]. 4 th ed. Beijing:Higher Education Press, 2004:195-196.(in Chinese)
• [5]邵怀华,卓玉霖.陀螺进动中的“角动量不守恒”问题[J].物理与工程,2018,28(6):39-42.SHAO H H, ZHUO Y L. The explanation of“non conservation of angular momentum” in gyroscope precession[J].Physics and Engineering, 2018, 28(6):39-42.(in Chinese)
• [6]张汉壮.力学[M].4版.北京:高等教育出版社.2019:147-148.ZHANG H Z. Mechanics[M]. 4 th ed. Beijing:Higher Education Press, 2019:147-148.(in Chinese)
• [7]刘贤雨.对称陀螺在重力场中定点转动的分析[J].大学物理,2020,39(8):51-57,67.LIU X Y. Analysis of the rotation modes of the symmetric top around fixed point in gravitational field[J]. College Physics, 2020, 39(8):51-57, 67.(in Chinese)
• [8]熊永建.基于解析结果的拉格朗日陀螺运动特性分析[J].大学物理,2023,42(2):1-5,17.XIONG Y J. Motion characteristics of Lagrange gyroscope based on analytical results[J]. College Physics, 2023,42(2):1-5, 17.(in Chinese)