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The stability of the Thomson heptagon

D. S. Schmidt
Journal / Anthology

Regular & Chaotic Dynamics
Year: 2004
Volume: 9
Issue: 4
Page range: 519-528

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.

*Science > Physics > Fluid Mechanics