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利用手机传感器测定刚体的惯性张量

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  • 北京师范大学 物理学系,北京 100875
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.

收稿日期: 2021-02-17

  修回日期: 2021-03-30

  网络出版日期: 2021-11-15

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

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  • Department of Physics,Beijing Normal University,Beijing 100875,China

Received date: 2021-02-17

  Revised date: 2021-03-30

  Online 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.

本文引用格式

楼晨煊, 周婧琳, 郑雪瑶, 刘珂溦, 罗丹楠, 白在桥 . 利用手机传感器测定刚体的惯性张量[J]. 大学物理, 2021 , 40(11) : 48 . DOI: 10.16854 / j.cnki.1000-0712.210079

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.

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