Far Eastern Mathematical Journal

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A study of relative equilibria of three vortices


A. I. Gudimenko, A. D. Zakharenko

2010, issue 2, Ñ. 106–116


Abstract
The positions of relative equilibrium of three point vortices on the unbounded plain according to their type and stability are fully classified.

Keywords:
point vortices, relative equilibria, stability, algebraic reduction

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References

[1] J. Tavantzis, L. Ting, “The dynamics of three vortices revisited”, Phys. Fluids, 31:6 (1988), 1392–1409.
[2] A. V. Borisov, I. S. Mamaev, Matematicheskie metody dinamiki vixrevyx struktur, In-t komp'yuter. issled., Moskva – Izhevsk, 2005.
[3] H. Aref, “Stability of relative equilibria of three vortices”, (Article 094101), Phys. Fluids, 21:9 (2009), 1–22.
[4] A. V. Borisov, A. E. Pavlov, “Dinamika i statika vixrej na ploskosti i sfere — I”, Reg. & Chaot. Dyn, 3:1 (1998), 28–38.
[5] A. V. Borisov, V. G. Lebedev, “Dinamika trex vixrej na ploskosti i na sfere — II. Obshhij kompaktnyj sluchaj”, Reg. & Chaot. Dyn, 3:2 (1998), 99–114.
[6] A. V. Borisov, V. G. Lebedev, “Dinamika trex vixrej na ploskosti i na sfere — III. Nekompaktnyj sluchaj. Problema kollapsa i rasseyaniya”, Reg. & Chaot. Dyn, 3:4 (1998), 74–86.
[7] A. I. Gudimenko, “Dinamika trex vixrej v vozmushhennoj singulyarnoj konfiguracii”, Nelinejnaya Dinamika, 4:2 (2008), 429–441.
[8] A. I. Gudimenko, “Dynamics of perturbed equilateral and collinear configurations of three point vortices”, Reg. & Chaot. Dyn, 13:2 (2008), 85–95.
[9] A. I. Gudimenko, K. G. Kupcov, “Dvizhenie trex tochechnyx vixrej v sluchae, esli odin iz nix proxodit cherez centr zavixrennosti”, Vestn. Udmurd. gos. un-ta, 2009, ¹ 2, 38–52.
[10] A. A. Andronov, E. A. Leontovich, I. I. Gordon, A. G. Majer, Kachestvennaya teoriya dinamicheskix sistem vtorogo poryadka, Nauka, Moskva, 1966.

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