球体在圆锥面上滚动

The rolling sphere and the quantum spin

We consider the problem of a sphere rolling of a curved surface and solve it by mapping it to the precession of a spin 1/2 in a magnetic field of variable magnitude and direction. The mapping can be of pedagogical use in discussing both rolling and spin precession, and in particular in understanding the emergence of geometrical phases in classical problems.

一个球体在一个静止球体的表面上运动，一个简单的phase diagram

A sphere moving down the surface of a static sphere and a simple phase diagram

将一个小球放在一个无摩擦力的大球的顶部，使其以$θ_{l}=\cos^{-1}{2/3}$的角度滑动。在另一个极端，如果大球体的表面具有静摩擦系数$μ_s\to\infty$，则小球体开始滚动并继续滚动，直到它以$θ_{l} =\cos^{-1}{10/17}$的角度离开表面。在这种情况下，$0\leqμ_s<\infty$，我们得到一个简单的相图。这三个阶段分别是纯滚动、滚动加滑动和脱离状态。一条相线将纯滚动与带滑动的滚动分开。当纯滚动的停止角相对于静摩擦系数$μ_s$作图时，得到该图。本文的研究仅限于可动球体从静止球体的顶部以无穷小的动能出发的情形。

不规则圆柱体和球体滚动中的相变

Phase transitions in rolling of irregular cylinders and spheres

将终端滚动速度作为序参量，研究不规则圆柱体和球体在斜面上滚动时由状态空间维度和惯性引发的相变，通过实验验证理论并揭示其与毛球定理及SO(3)拓扑性质的关联。

Slipping and Rolling on an Inclined Plane

In the first part of the article using a direct calculation two-dimensional motion of a particle sliding on an inclined plane is investigated for general values of friction coefficient ($μ$). A parametric equation for the trajectory of the particle is also obtained. In the second part of the article the motion of a sphere on the inclined plane is studied. It is shown that the evolution equation for the contact point of a sliding sphere is similar to that of a point particle sliding on an inclined plane whose friction coefficient is $2/7}\ μ$. If $μ> 2/7 \tanθ$, for any arbitrary initial veloci…

球体在发散斜轨上的滚动

Spheroid rolling up on diverging inclines

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。

死亡领域内的圆形轨道

Circular Orbits Inside the Sphere of Death

在均匀引力场中，在球体内侧滚动而不滑动的轮子或球体可以有完全位于“赤道”上方的稳定圆形轨道，而自由滑动的粒子则不能。