Spirographic motion in a vortex
Sumithra Reddy Yerasi, Rama Govindarajan, Dario Vincenzi
Abstract
The present study investigates the dynamics of an inertialess rigid dumbbell in a steady two-dimensional vortex. This system goes beyond the point-particle approximation but remains analytically solvable. For any vortex, the dynamics of the dumbbell follows from the existence of a constant of motion that is independent of the form of the vortex. In particular, if the fluid angular velocity decreases with the radial distance, the dumbbell performs spirographic trajectories around the vortex center, the shape of which is highly sensitive to the initial position and orientation of the dumbbell.
Topics & Concepts
DumbbellVortexPhysicsOrientation (vector space)Classical mechanicsMotion (physics)Angular velocityConstant angular velocityDynamics (music)Vortex ringVorticityMechanicsPosition (finance)Point (geometry)GeometryMathematicsBiologyEconomicsFinanceAcousticsPhysiologyParticle Dynamics in Fluid FlowsFluid Dynamics and Turbulent FlowsMicro and Nano Robotics