Regular polygon solutions of the 𝑁-body problem

Perko, L. M.; Walter, E. L.

doi:10.1090/S0002-9939-1985-0784183-1

Regular polygon solutions of the $N$-body problem
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by L. M. Perko and E. L. Walter PDF

Proc. Amer. Math. Soc. 94 (1985), 301-309 Request permission

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 $N \geqslant 4,N$ 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 $N$-body problem if and only if the masses are equal.

References

Erweiterung der bekannten Speciallösung des Dreikörperproblems

64

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