Movement of solid filaments in axisymmetric fluid flow

We consider the movement of slender toroidal filaments immersed in a 3D fluid described by the incompressible Euler equations. The filaments are described by Newtonian mechanics and interact with the fluid through the pressure exerted at the boundary. We assume that the filaments are almost rigid in the sense that the only non-rigid movement they can undergo is a change of length and that the fluid is irrotational, but can have a nonzero circulation around the filaments. We show that this kind of system can be described through an ODE in the positions of the bodies and that in the limit, where the bodies shrink to massless filaments, the system converges to an ODE system similar to the dynamics of the corresponding vortex filaments.