标题： 摩擦性最速降线 显示英文标题

标题： The Frictional Brachistochrone

摘要： 这里，我为一种具有库仑摩擦耗能的颗粒材料质点运动构造了一个优美的摩擦变分问题，该问题固有地包含了路径曲率的变化。 这个简单模型揭示了几种显著的力学现象。 它适用于任何摩擦粒子。 随着摩擦力的增加，粒子路径变得越来越直，直到在足够高的摩擦极限下达到直线变分问题。 直线变分问题的存在是令人惊叹的。 考虑了摩擦变分问题的一些潜在工业应用。 显示英文摘要

摘要： Here, I construct an elegant frictional brachistochrone for a mass point motion of a granular material with the Coulomb frictional energy dissipation that inherently includes the evolving path curvature. The simple model reveals several striking mechanical phenomena. It is applicable to any frictional particle. With increasing friction, the particle path becomes less and less curved until a straight brachistochrone is attained in the limit of sufficiently high friction. The existence of the straight-brachistochrone is phenomenal. Some potential industrial applications of the frictional brachistochrone are considered.