大学物理 ›› 2021, Vol. 40 ›› Issue (11): 48-.doi: 10.16854 / j.cnki.1000-0712.210079

• 大学生园地 • 上一篇    下一篇

利用手机传感器测定刚体的惯性张量

楼晨煊,周婧琳,郑雪瑶,刘珂溦,罗丹楠,白在桥   

  1. 北京师范大学 物理学系,北京 100875
  • 收稿日期:2021-02-17 修回日期:2021-03-30 出版日期:2021-11-20 发布日期:2021-11-15
  • 通讯作者: 白在桥,E-mail: baizq@ bnu.edu.cn
  • 作者简介:楼晨煊( 1999—) ,男,浙江余姚人,北京师范大学物理学系 2018 级本科生.

Measurement of rigid body inertia tensor using gyroscope sensor on a mobile phone

LOU Chen-xuan,ZHOU Jing-lin,ZHENG Xue-yao,LIU Ke-wei,LUO Dan-nan,BAI Zai-qiao   

  1. Department of Physics,Beijing Normal University,Beijing 100875,China
  • Received:2021-02-17 Revised:2021-03-30 Online:2021-11-20 Published:2021-11-15

摘要: 利用手机陀螺仪传感器和 phyphox 软件,记录手机在空中自由旋转时的角速度曲线,根据质心系中的总角动量和机械能守恒,可以确定手机惯性张量的相对值. 在惯性张量的非对角元素为零的假设下,得到了对角元素相对值的解析表达式.如果考虑非对角元素,则可以用梯度下降算法求解,将结果代入欧拉动力学方程,验证了其正确性.

关键词: 惯性张量, phyphox, 陀螺仪, 欧拉方程

Abstract: By using a gyroscope sensor and phyphox software,the angular velocity curve of a free

falling mo- bile phone is recorded. Then,up to a scale constant,the inertia tensor of the

phone is determined based on the conservation of orbital angular momentum and kinetic energy

in the center-of-mass reference frame. Depending on whether vanishing off-diagonal elements is or

not assumed,two algorithms are proposed to calculate the inertia ten- sor. The results are

confirmed by substituting it into the Euler equation for recoded trajectories.

Key words: rotation inertia, phyphox, gyroscope, euler equation