AI 中文总结
本文研究发散斜轨上刚体向上滚动的反直觉现象，扩展双圆锥悖论至球体、椭球体等刚体，推导其运动的几何与能量约束并通过实验验证理论模型。
AI 中文摘要
在发散斜轨上向上滚动的物体表现出一种违反直觉的行为，这一现象一直吸引着物理学家和学生的兴趣。其中最著名的是双圆锥悖论，即圆锥因轨道几何结构而看似向上滚动。本文将这一概念扩展到更一般的刚体，包括球体和椭球体，研究该运动发生的物理条件，运用分析力学推导必要的几何和能量约束，并通过精心设计的实验验证理论模型。
英文摘要
Objects rolling upward on diverging inclined rails exhibit a counterintuitive behavior that has intrigued physicists and students alike. Among the most well-known is the double-cone paradox, where a cone appears to roll uphill due to the geometry of the rails. In this paper, we extend this idea to more general rigid bodies, including spheres and ellipsoids. We examine the physical conditions under which this motion occurs, and we derive the necessary geometric and energetic constraints using analytical mechanics. We then validate our theoretical models through carefully designed experiments.
Comments9 pages, 12 figures
