Regular and Chaotic Dynamics

, Volume 23, Issue 5, pp 569–579

# Stationary Configurations of Point Vortices on a Cylinder

• Dariya V. Safonova
• Maria V. Demina
• Nikolai A. Kudryashov
Article

## Abstract

In this paper we study the problem of constructing and classifying stationary equilibria of point vortices on a cylindrical surface. Introducing polynomials with roots at vortex positions, we derive an ordinary differential equation satisfied by the polynomials. We prove that this equation can be used to find any stationary configuration. The multivortex systems containing point vortices with circulation Γ1 and Γ22 = −μΓ1) are considered in detail. All stationary configurations with the number of point vortices less than five are constructed. Several theorems on existence of polynomial solutions of the ordinary differential equation under consideration are proved. The values of the parameters of the mathematical model for which there exists an infinite number of nonequivalent vortex configurations on a cylindrical surface are found. New point vortex configurations are obtained.

## Keywords

point vortices stagnation points stationary configuration vortices on a cylinder polynomial solution of differential equation

33D45 76M23

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## Authors and Affiliations

• Dariya V. Safonova
• 1
• Maria V. Demina
• 1
• Nikolai A. Kudryashov
• 1
1. 1.Department of Applied MathematicsNational Research Nuclear University MEPhIMoscowRussia