论文标题
弹性杆的平面平衡，缠绕在圆形的capstan上
Planar equilibria of an elastic rod wrapped around a circular capstan
论文作者
论文摘要
我们介绍了一项关于包裹在刚性圆形capstan上的末端弹性杆的平面平衡的研究。杆和卡普斯坦之间的无摩擦和摩擦接触都被考虑。我们确定了三个无摩擦接触的情况 - 即杆沿连续弧和两个点触摸卡普斯坦的位置。我们表明，与完全柔韧的细丝相反，包裹在capstan上的\ emph {有限长度}的弹性杆不需要摩擦以支撑其两端的不等载荷。此外，我们将对应于上述三个情况的杆平衡分类为杆的长度远大于卡普斯坦半径的极限。在相同的极限下，我们结合了杆和卡普斯坦之间的摩擦相互作用，并计算杆的限制平衡。我们对摩擦情况的解决方案充分概括了\ emph {经典的Capstan问题}，包括有限厚度和包裹在圆形capstan周围的柔性丝的弯曲弹性的效果。
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.
