刚性球体在转动环形凹槽内的动力学行为

Dynamics of a rigid sphere on a rotating annular groove

本文研究了刚性球体在绕竖直轴旋转的圆环形槽中的运动情况,发现球体的自转与公转通过摩擦力相互耦合.理论上,给出了球平衡位置随圆环角速度增加的具体关系,并得到了球在环中具有阻尼振荡特征的动力学行为.实验上,本文通过3D打印搭建了实验装置,结合所提出的一种测量圆弧面与物体摩擦系数的方法,定量验证了理论的若干预言.

In this paper,the dynamics and trajectory of a rigid sphere in an annular groove rotating around a vertical axis is studied.The rotation and revolution of the sphere are coupled with each other through friction.Theoretically,the balance position of the sphere which monotonically increases with the rotating speed of the annular groove is obtained.And the damped oscillation of the sphere is solved numerically.In addition,an experimental setup is built with the help of 3D printing,and a method is proposed for measuring friction coefficient between the arc surface and the object thereon.The theoretical predictions are quantitatively verified by the experimental results.