The dynamical system governing the motion of a curved rigid two-dimensional
circular-arc fiber in simple shear is derived in analytical form. This is achieved by
finding the solution for the associated low-Reynolds-number flow around such a fiber
using the methods of complex analysis. Solutions of the dynamical system display
the “flipping” and “scooping” recently observed in computational studies of threedimensional
fibers using linked rigid rod and bead-shell models [Wang et al, Phys.
Fluids, 24, (2012)]. To complete the Jeffery-type equations for a curved fiber in a
linear flow field we also derive its evolution equations in an extensional flow. It is
expected that the equations derived here also govern the motion of slender, curved,
three-dimensional rigid fibers when they evolve purely in the plane of shear or strain.