On the existence of certain configurations of relative equilibrium in the n-body problem

Details On the existence of certain configurations of relative equilibrium in the n-body problem On the existence of certain configurations of relative equilibrium in the n-body problem

Jan 1987

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1987crasb.304..161e&link_type=abstract

Academie des Sciences (Paris), Comptes Rendus, Serie II Mecanique, Physique, Chimie, Sciences de l'Univers, Sciences de la Terre

Physics

Celestial Mechanics, Many Body Problem, Newton Theory, Equations Of Motion, Gravitational Effects, Hamiltonian Functions, Polygons, Systems Stability

Scientific paper

The problem of n bodies submitted to mutual Newtonian attractions is considered, and it is proposed that configurations of relative equilibrium for n bodies at the vertices of a regular polygon with n sides exist for n greater than or equal to 4 if and only if the masses are equal. This result has been previously demonstrated for n equal to 4 and 5, and a general proof for n greater than or equal to 4 is given. It is noted that previous results for n = 3 (Elmabsout, 1978; Wintner, 1941) show relative equilibrium conditions to exist for bodies at the vertices of an equilateral triangle without conditions on the masses.

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