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首页> 外文期刊>European journal of physics: A journal of the European Physical Society >Analysis of the wobbling effect in a lens-shaped body rotation
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Analysis of the wobbling effect in a lens-shaped body rotation

机译：透镜形体旋转中的摆动效应分析

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摘要

We discuss the wobbling motion in a lens-shaped body rotation, focusing on the frequencies and the amplitude of nutation by filming the rotational motion and wobbling of the body. The friction coefficient of the surface is altered to examine its influence for two lenses with different. curvature radii. MATLAB programs are developed to retrieve the Euler angles, which are graphed according to time. It is shown that the lens with a smaller curvature radius exhibits the wobbling effect in all cases, whereas the lens with a larger curvature radius shows such behaviour in limited circumstances. The study confirms that the friction coefficient has a negative linear correlation with the vertical axis declination amplitude with the R-squared value 0.878, showing that friction gives damping and causes smaller axis declination amplitudes. Negative linear correlation also exists with relation to the number of wobbles before the motion stops, where the R-squared value is 0.938, providing further evidence that friction and wobbling cause higher energy dissipation rates. The frequency of the wobbling motion only has a correlation with the curvature radius of the lens, showing no explicit correlation with the friction coefficient, with its R-squared value being 0.077. No losses of contact were observable in this motion. The overall process does not utilize particularly expensive apparatus and will be applicable for senior undergraduate students to experiment on and analyze the motion of a special situation regarding a rigid body that is both spinning and nutating.
机译：我们在透镜形体旋转中讨论摆动运动，通过拍摄身体的旋转运动和摆动来聚焦频率和弯矩的振幅。表面的摩擦系数被改变以检查其对两个透镜的影响。曲率半径。开发MATLAB程序以检索欧拉角，根据时间进行图。结果表明，具有较小曲率半径的镜片在所有情况下表现出摆动效果，而具有较大曲率半径的透镜在有限的情况下示出了这种行为。该研究证实，摩擦系数与垂直轴线倾幅幅度的负线性相关性与R线值0.878具有负线性相关性，表明摩擦产生阻尼并导致较小的轴线倾斜幅度。负线性相关性也存在于运动停止前的摆动次数的关系，其中R方形值为0.938，提供进一步的证据，即摩擦和摆动导致更高的能量耗散速率。摆动运动的频率仅与透镜的曲率半径有关，显示与摩擦系数没有明确的相关性，其R线值为0.077。在这项运动中没有观察到接触损失。整体过程不利用特别昂贵的设备，适用于高级本科生来试验和分析特殊情况的运动，这是一种刚体旋转和核对的刚体。

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