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A new collision-based periodic orbit in the three-dimensional eight-body problem

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Abstract

We construct a highly-symmetric periodic orbit of eight bodies in three dimensions. In this orbit, each body collides with its three nearest neighbors in a regular periodic fashion. Regularization of the collisions in the orbit is achieved by an extension of the Levi-Civita method. Initial conditions for the orbit are found numerically. Linear stability of the orbit is then shown using a technique by Roberts. Evidence toward higher-order stability is presented as an additional result of a numerical calculation.

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All data generated or analyzed during this study are included in this published article.

Notes

  1. https://physics.nist.gov/cuu/Constants/index.html.

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Acknowledgements

I am grateful for all the referee reports which helped to improve the content and readability of the paper. I wish to dedicate this paper to my wife, who has brought a new dimension of joy to my life.

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  1. Department of Mathematics, Utah Valley University, Orem, UT, 84058, USA

    Skyler Simmons

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Simmons, S. A new collision-based periodic orbit in the three-dimensional eight-body problem. Celest Mech Dyn Astron 134, 54 (2022). https://doi.org/10.1007/s10569-022-10109-0

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