Planar equilibria of an elastic rod wrapped around a circular capstan
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 finite length wrapped around a capstan does not require friction to support unequal loads at its two ends.