标题： 平面弹性杆环绕圆形卷筒的平衡状态 显示英文标题

标题： Planar equilibria of an elastic rod wrapped around a circular capstan

摘要： 我们研究了终端加载的弹性杆环绕刚性圆柱帽状物时的平面平衡状态。考虑了杆与帽状物之间无摩擦和有摩擦的接触情况。我们确定了三种无摩擦接触的情况——即杆与帽状物在一个点、沿着连续弧线以及在两个点接触。我们表明，与完全柔性的细丝不同，一根长度为\emph{有限长度}的弹性杆环绕帽状物时不需要摩擦力来支撑两端不同的载荷。此外，在杆的长度远大于帽状物半径的极限情况下，我们将对应于上述三种情况的杆平衡状态进行了分类。在同一极限情况下，我们纳入了杆与帽状物之间的摩擦相互作用，并计算了杆的极限平衡状态。我们对摩擦情况的解决方案完全推广了\emph{经典的缆车问题}，以包括柔性细丝有限厚度和弯曲弹性的效应，该细丝环绕一个圆形帽状物。 显示英文摘要

摘要： We present a study on planar equilibria of a terminally loaded elastic rod wrapped around a rigid circular capstan. Both frictionless and frictional contact between the rod and the capstan are considered. We identify three cases of frictionless contact -- namely where the rod touches the capstan at one point, along a continuous arc, and at two points. We show that, in contrast to a fully flexible filament, an elastic rod of \emph{finite length} wrapped around a capstan does not require friction to support unequal loads at its two ends. Furthermore, we classify rod equilibria corresponding to the three aforementioned cases in a limit where the length of the rod is much larger than the radius of the capstan. In the same limit, we incorporate frictional interaction between the rod and the capstan, and compute limiting equilibria of the rod. Our solution to the frictional case fully generalizes the \emph{classic capstan problem} to include the effects of finite thickness and bending elasticity of a flexible filament wrapped around a circular capstan.