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.

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