On the regular-geometric-figure solution to the N-body problem

Details On the regular-geometric-figure solution to the N-body problem On the regular-geometric-figure solution to the N-body problem

2001-07-04

arxiv.org/abs/physics/0107004v1

Physics

Classical Physics

To appear in Eur. J. Phys. (5 pages)

Scientific paper

10.1088/0143-0807/22/5/304

The regular-geometric-figure solution to the $N$-body problem is presented in a very simple way. The Newtonian formalism is used without resorting to a more involved rotating coordinate system. Those configurations occur for other kinds of interactions beyond the gravitational ones for some special values of the parameters of the forces. For the harmonic oscillator, in particular, it is shown that the $N$-body problem is reduced to $N$ one-body problems.

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