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This question is part of this week's Journal Club session.

These systems look ridiculously fun to construct. Could someone explain the particulars? What are the various types of solutions, and what are their dynamics? How are they different from previously discovered solutions?

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It's been a while since I first saw the article, which is described nicely in

Physicists Discover a Whopping 13 New Solutions to Three-Body Problem. Jon Cartwright, Science Now news, 8 March 2013.

The original paper is at

Three Classes of Newtonian Three-Body Planar Periodic Orbits. Milovan Šuvakov and V. Dmitrašinović. Phys. Rev. Lett. 110 no. 11, 114301 (2013). arXiv:1303.0181.

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The article you posted contains the following reference:

Milovan Šuvakov and Veljko Dmitrašinović, Phys. Rev. Lett., (2013)

I imagine you will find all the particulars you need in the arXiv preprint of that paper.

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