  We consider a model that approximates vortex rings in the axisymmetric 3D
Euler equation by the movement of almost rigid bodies described by Newtonian
mechanics. We assume that the bodies have a circular cross-section and that the
fluid is irrotational and interacts with the bodies through the pressure
exerted at the boundary. 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 point vortex system. In particular, we can show that in a
suitable set-up, the bodies perform a leapfrogging motion.
