Stability of relative equilibria in the problem of N + 1 vortices

SIAM Journal on Mathematical Analysis

Volumn 31, Issue 2, 2000, Pages 231-250

  Cabral, H E ^a   Schmidt, D S ^b  

^a FEDERAL UNIVERSITY OF PERNAMBUCO   (Brazil)

^b University of Cincinnati   (United States)

Author keywords

Relative equilibria; Spectral stability; Vortices

Indexed keywords

EID: 0033474942     PISSN: 00361410     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0036141098302124     Document Type: Article

References (13)

1. H. AREF, On the equilibrium and stability of a row of point vortices, J. Fluid Mech., 290 (1995), pp. 167-181.
2. L. G. KHAZIN, Regular polygons of point vortices and resonance instability of steady states, Soviet Phys. Dokl., 21 (1976), pp. 567-569.
3. G. KIRCHHOFF, Mechanik, Vorlesungen über Mathematische Physik, Teubner, Leipzig, 1883.
4. D. LEWIS AND T. RATIU, Polygonal vortex configurations, in New Trends for Hamiltonian Systems and Celestial Mechanics, Vol. 8, E. A. Lacomba and J. Llibre, eds., World Scientific, Singapore, 1996, pp. 249-262.
5. J. C. MAXWELL, Stability of the motion of Saturn's rings, in Maxwell on Saturn's Rings, S. Brush, C. W. F. Everitt, and E. Garber, eds., MIT Press, Cambridge, MA, 1983.
6. G. J. MERTZ, Stability of body-centered polygonal configurations of ideal vortices, Phys. Fluids, 21 (1978), pp. 1092-1095.
7. K. R. MEYER AND D. S. SCHMIDT, Bifurcations of relative equilibria in the N-body and Kirchhoff problems, SIAM J. Math. Anal., 19 (1988), pp. 1295-1313.
8. R. MOECKEL, Linear stability analysis of some symmetrical classes of relative equilibria, in Hamiltonian Dynamical Systems, History, Theory, and Applications, H. S. Dumas, K. R. Meyer, and D. S. Schmidt, eds., IMA Vol. Math. Appl. 68, Springer, New York, 1994, pp. 291-317.
9. G. K. MORIKAWA AND E. V. SWENSON, Interacting motion of rectilinear geostrophic vortices, Phys. Fluids, 14 (1971), pp. 1058-1073.
10. W. OLVA, The motion of two dimensional vortices with mass as a singular perturbation Hamiltonian problem, in New Trends for Hamiltonian Systems and Celestial Mechanics, Vol. 8, E. A. Lacomba and J. Llibre, eds., World Scientific, Singapore, 1996, pp. 301-310.
11. J. I. PALMURE, Measure of degenerate relative equilibria I, Ann. Math., 140 (1976), pp. 421-429.
12. D. S. SCHMIDT, Spectral stability of relative equilibria in the N + 1 body problem, in Hamiltonian Systems and Celestial Mechanics, E. A. Lacomba and J. Llibre, eds., World Scientific, Singpore, 1995, pp. 321-341.
13. J. J. THOMSON, A Treatise on the Motion of Vortex Rings: An Essay to which the Adams Prize was Adjusted in 1882, University of Cambridge, Macmillan, London, 1883.