Easwar K, Rouyer F, Menon Narayanan
Department of Physics, University of Massachusetts, Amherst, Massachusetts 01003, USA.
Phys Rev E Stat Nonlin Soft Matter Phys. 2002 Oct;66(4 Pt 2):045102. doi: 10.1103/PhysRevE.66.045102. Epub 2002 Oct 21.
The final stages of a coin spinning on a flat surface have recently been proposed [H.K. Moffatt, Nature (London) 404, 833 (2000)] as an example of a finite-time singularity, wherein the precession rate of the symmetry axis of the coin diverges as it comes to a stop. We report measurements by high-speed video imaging of the rolling motion of disks and rings on a variety of surfaces. We find that the precession rate, Omega, diverges as a power law in time: Omega(t) proportional, variant (t-t(o))(-1/n), where t(o) is the instant the motion ceases. The exponent n varies between 2.7 and 3.2 under different experimental conditions. The value of n, as well as the systematic dependence of precession rate on coefficients of friction, establishes that the primary mechanism of energy dissipation is rolling friction rather than air drag, as previously suggested.
最近有人提出[H.K.莫法特，《自然》（伦敦）404, 833 (2000)]，硬币在平面上旋转的最后阶段是有限时间奇点的一个例子，其中硬币对称轴的进动速率在其停止时发散。我们报告了通过高速视频成像对圆盘和圆环在各种表面上滚动运动的测量结果。我们发现，进动速率Ω随时间呈幂律发散：Ω(t)∝(t - tₒ)^(-1/n)，其中tₒ是运动停止的瞬间。在不同的实验条件下，指数n在2.7到3.2之间变化。n的值以及进动速率对摩擦系数的系统依赖性表明，能量耗散的主要机制是滚动摩擦，而不是如先前所认为的空气阻力。
