Abstract
We consider the planar problem of three bodies which attract mutually with the force proportional to a certain negative integer power of the distance between the bodies. We show that such generalisation of the gravitational three-body problem is not integrable in the Liouville sense.
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Acknowledgments
This research has been partially supported by grant No. N N202 2126 33 of Ministry of Science and Higher Education of Poland and by EU funding for the Marie-Curie Research Training Network AstroNet.
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Open Access This is an open access article distributed under the terms of the Creative Commons Attribution Noncommercial License (https://creativecommons.org/licenses/by-nc/2.0), which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.
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Maciejewski, A.J., Przybylska, M. Non-integrability of the three-body problem. Celest Mech Dyn Astr 110, 17–30 (2011). https://doi.org/10.1007/s10569-010-9333-z
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DOI: https://doi.org/10.1007/s10569-010-9333-z