投掷无弹跳厚硬币的概率和动力学
Probability and dynamics in the toss of a non-bouncing thick coin
摘要：
当一个厚的圆柱形硬币被抛向空中，并在没有弹性的基底上反弹时，它最终会正面或侧面。我们考虑了自旋和进动的刚体动力学，并计算了厚硬币的头部、尾部和侧面的概率分布，作为其尺寸和初始条件分布的函数。我们的理论产生了一个简单的表达式的长宽比均匀的硬币与规定的频率的头/尾相比，双方，我们验证了投掷实验，使用不同的长宽比的硬币。
英文摘要：
When a thick cylindrical coin is tossed in the air and lands without bouncing on an inelastic substrate, it ends up on its face or its side. We account for the rigid body dynamics of spin and precession and calculate the probability distribution of heads, tails, and sides for a thick coin as a function of its dimensions and the distribution of its initial conditions. Our theory yields a simple expression for the aspect ratio of homogeneous coins with a prescribed frequency of heads/tails compared to sides, which we validate by tossing experiments using coins of different aspect ratios.
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