This article is cited in 5 papers

Effective computations in modern dynamics

The stability of the Thomson heptagon

D. S. Schmidt

Department of Electrical & Computer Engineering and Computer Science, University of Cincinnati, 894 Rhodes Hall, Cincinnati, USA 45221-0030

Abstract: In 1882 J. J. Thomson had claimed in his Adams prize essay "The motion of vortex rings" that a ring of seven vortices would be unstable. It was shown later that linear analysis can not decide stability in this case. In 1999 Cabral and Schmidt proved stability by calculating the higher order terms in the normal form of the Hamiltonian with the help of POLYPACK, a personal algebraic processor. The work is repeated here with the help of the more readily available computer algebra system MATHEMATICA.

MSC: 76B47, 34K18, 34K20

Received: 04.06.2004

Language: English

DOI: 10.1070/RD2004v009n04ABEH000294

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