Year: 2018
Type: article
Abstract: We consider the equations of motion of n vortices of equal circulation in the plane, in a disk and on a sphere. The vortices form a polygonal equilibrium in a rotating frame of reference. We use numerical continuation in a boundary value setting to determine the Lyapunov families of periodic orbits that arise from the polygonal relative equilibrium. When the frequency of a Lyapunov orbit and the frequency of the rotating frame have a rational relationship, the orbit is also periodic in the inertial frame. A dense set of Lyapunov orbits, with frequencies satisfying a Diophantine equation, corresponds to choreographies of n vortices. We include numerical results for all cases, for various values of n , and we provide key details on the computational approach.
Source: Regular and Chaotic Dynamics
Institutions: Universidad Nacional Autónoma de México, Concordia University
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2896883450