Spirographic motion in a vortex

The present study investigates the dynamics of an inertialess rigid dumbbell in a steady two-dimensional vortex. This system goes beyond point-particle approximation but remains analytically solvable. For any vortex, follows from existence constant motion that is independent form In particular, if fluid angular velocity decreases with radial distance, performs spirographic trajectories around vortex center, shape which highly sensitive to initial position and orientation dumbbell.