Nonlinear physics and mechanics

The Motion of an Elliptic Foil in the Field of a Fixed Vortex Source

E. M. Artemova, D. A. Lagunov, E. V. Vetchanin

Udmurt State University, ul. Universitetskaya 1, Izhevsk, 426034 Russia

Abstract: This paper is concerned with the motion of an elliptic foil in the field of a fixed point singularity. A complex potential of the fluid flow is constructed, and the forces and the torque which act on the foil from the fluid are obtained. It is shown that the equations of motion of the elliptic foil in the field of a fixed point vortex source can be represented as Lagrange – Euler equations. It is also shown that the system has an additional first integral due to the conservation of the angular momentum. An effective potential of the system under consideration is constructed. For the cases where the singularity is a vortex or a source, unstable relative equilibrium points corresponding to the circular motion of the foil around the singularity are found.

Keywords: ideal fluid, elliptic foil, point vortex, point source, Lagrangian form, Hamiltonian form

MSC: 37J60, 34A34

Received: 30.09.2024
Accepted: 25.11.2024

Language: English

DOI: 10.20537/nd241203