标题： 在复杂性的边缘：最简单的非简单耦合机械系统 显示英文标题

标题： On the edge of complexity: The simplest not simple coupled mechanical system

摘要： 我们证明，在由一个圆环和一个圆柱体通过理想弹簧连接其中心的振荡系统中，其质心不会保持静止。 这种效应是由于作用在系统上的合力静摩擦力引起的，当耦合的刚体具有相同的转动惯量时，这种力会消失。 然而，当通过适当定位弹簧的两个固定端点垂直方向时，如果转动惯量不同，可以证明系统的质心保持静止。 耦合系统的运动方程是通过动力学方程、拉格朗日方程、哈密顿方程以及应用能量和角动量守恒定律推导出来的。 还研究了作用在刚体上的静摩擦力之间的关系。 显示英文摘要

摘要： We show that during normal modes of an oscillatory system consisting of a hoop and a cylinder joining their centers by an ideal spring, its central mass does not remain at rest. This effect is due to the resultant external static friction forces acting on the system which disappears when the coupled rigid bodies have the same moment of inertia. However, in case of different moment of inertia by proper positioning the two fixed end points of the spring vertically, it is shown that the central mass of the system remains at rest. The equation of motion of the coupled system is derived using dynamic equations, Lagrange's equations, Hamilton's equations and even by applying the conservation laws of energy and angular momentum. The relationship between the static friction forces acting on the rigid bodies is also examined.