空气阻力控制欧拉盘的有限时间奇点
Air Drag Controls the Finite-Time Singularity of Euler's Disk
AI总结：
研究揭示了欧拉盘在停止过程中，空气阻力主导了奇点前的晚期运动，而早期则由滚动摩擦主导，揭示了低负载光滑表面滚动接触系统的耗散机制。
摘要：
一个盘在被侧翻后停止旋转的运动是有限时间奇点的经典例子，但主导这一过程的耗散机制仍存在争议。利用立体高速摄影，我们研究了不同质量和半径的盘在不同表面的动态行为。我们显示，奇点附近的晚期运动由边界层下剪切引起的粘性空气阻力主导，这通过动态质量依赖性、部分真空中的测量以及使用钢环的几何控制得到证实。在更早的时间，耗散主要由滚动摩擦主导，这在玻璃上表现出与盘质量无关的亚线性缩放，表明了基于粘附的滚动阻力。这些结果澄清了欧拉盘奇点背后的耗散机制，并对在低负载下在光滑表面上运行的滚动接触系统具有更广泛的意义。
英文摘要：
The motion of a disk spinning to rest after being tipped on its side is a classic example of a finite-time singularity, yet the dominant dissipation mechanism governing this process remains debated. Using stereoscopic high-speed imaging, we study the dynamics of disks with varying mass and radius on different surfaces. We show that the late-time motion near the singularity is governed by viscous air-drag arising from shear in the boundary layer beneath the disk, as evidenced by the mass dependence of the dynamics, measurements in a partial vacuum, and a geometric control using a steel ring. At earlier times, dissipation is dominated by rolling friction, which on glass exhibits an unexpected sublinear scaling with disk mass, suggesting an adhesion-based rolling resistance. These results clarify the dissipation mechanisms underlying the singularity of Euler's disk and have broader implications for rolling-contact systems operating under low loads on smooth surfaces.
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