  We investigate the motion of a thin rigid body in Stokes flow and the
corresponding slender body approximation used to model sedimenting fibers. In
particular, we derive a rigorous error bound comparing the rigid slender body
approximation to the classical PDE for rigid motion in the case of a closed
loop with constant radius. Our main tool is the slender body PDE framework
established by the authors and D. Spirn in [18,19], which we adapt to the rigid
setting.
