在存在frictional forces的情况下，颗粒在转盘上滑动
Particle sliding on a turntable in the presence of frictional forces
摘要：
研究了点粒子在转盘上滑动的运动。运动方程推导出假设表施加摩擦力的颗粒上，这是恒定的大小和方向相反的运动的颗粒相对于转盘的方向。在用无量纲变量表示方程后，讨论了解的一些一般性质。近似的解析解的情况下，其中（i）的颗粒是从休息释放相对于实验室框架，（ii）的颗粒是从休息释放相对于转盘。然后对方程进行数值求解，以更全面地了解运动。人们发现，可以定义一个逃逸速度的粒子，这是所需的最小速度，使粒子移动到无穷远。逃逸速度是到转台中心的距离的函数，并且对于到中心的给定距离，逃逸速度取决于初始速度的方向。用虚拟力的概念对这种现象作了定性的解释。数值研究还指出了一种测量颗粒与转盘之间摩擦系数的替代方法。
英文摘要：
Motion of a point particle sliding on a turntable is studied. The equations of motion are derived assuming that the table exerts frictional force on the particle, which is of constant magnitude and directed opposite to the direction of motion of the particle relative to the turntable. After expressing the equations in terms of dimensionless variables, some of the general properties of the solutions are discussed. Approximate analytic solutions are found for the cases in which (i) the particle is released from rest with respect to the lab frame and, (ii) the particle is released from rest with respect to the turntable. The equations are then solved numerically to get a more complete understanding of the motion. It is found that one can define an escape speed for the particle which is the minimum speed required to get the particle to move off to infinity. The escape speed is a function of the distance from the center of the turntable and for a given distance from the center, it depends on the direction of initial velocity. A qualitative explanation of this behavior is given in terms of the fictitious forces. Numerical study also indicates an alternative way for measuring the coefficient of friction between the particle and the turntable.
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