Linear Stability in the 1 + N-Gon Relative Equilibrium

Details Linear Stability in the 1 + N-Gon Relative Equilibrium Linear Stability in the 1 + N-Gon Relative Equilibrium

Oct 2000

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2000hscm.conf..303r&link_type=abstract

HAMILTONIAN SYSTEMS AND CELESTIAL MECHANICS (HAMSYS-98). Proceedings of the III International Symposium. Held 7-11 December 1998

Physics

6

Scientific paper

We study the linear stability of the relative equilibrium in the n-body problem consisting of n equal masses at the vertices of a regular n-gon with an additional body of mass m at the center. This configuration is shown to be linearly unstable when n ≤ 6. For n ≥ 7, a value hn is found such that the configuration is linearly stable if and only if m > hn. This value is shown to increase proportionately to n3.

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