Abstract
In 1772, Lagrange showed that three masses at the vertices of an equilateral triangle, rotating about their common center of mass with an appropriate angular velocity, describe a periodic solution of the three-body problem. In this paper it is shown that for N ⩾ 4 , N N \geqslant 4,N masses at the vertices of a regular polygon, rotating about their common center of mass with an appropriate angular velocity, describe a periodic solution of the N N -body problem if and only if the masses are equal.
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