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A Database of High Precision Trivial Choreographies for the Planar Three-Body Problem

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Numerical Methods and Applications (NMA 2022)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 13858))

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Abstract

Trivial choreographies are special periodic solutions of the planar three-body problem. In this work we use a modified Newton’s method based on the continuous analog of Newton’s method and a high precision arithmetic for a specialized numerical search for new trivial choreographies. As a result of the search we computed a high precision database of 462 such orbits, including 397 new ones. The initial conditions and the periods of all found solutions are given with 180 correct decimal digits. 108 of the choreographies are linearly stable, including 99 new ones. The linear stability is tested by a high precision computing of the eigenvalues of the monodromy matrices.

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Acknowledgements

We greatly thank for the opportunity to use the computational resources of the “Nestum” cluster, Sofia, Bulgaria. We would also like to thank Veljko Dmitrashinovich from Institute of Physics, Belgrade University, Serbia for a valuable e-mail discussion and advice, and his encouragement to continue our numerical search for new periodic orbits.

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Authors and Affiliations

  1. Faculty of Mathematics and Informatics, Sofia University “St. Kliment Ohridski”, Sofia, Bulgaria

    I. Hristov & R. Hristova

  2. Institute of Information and Communication Technologies, Bulgarian Academy of Sciences, Sofia, Bulgaria

    R. Hristova

  3. Meshcheryakov Laboratory of Information Technologies, Joint Institute for Nuclear Research, Dubna, Russia

    I. Puzynin, T. Puzynina, Z. Sharipov & Z. Tukhliev

Authors
  1. I. Hristov
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  2. R. Hristova
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  3. I. Puzynin
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  4. T. Puzynina
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  5. Z. Sharipov
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  6. Z. Tukhliev
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Corresponding author

Correspondence to I. Hristov .

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Editors and Affiliations

  1. Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, Sofia, Bulgaria

    Ivan Georgiev

  2. Institute of Mechanics, Bulgarian Academy of Sciences, Sofia, Bulgaria

    Maria Datcheva

  3. Institute of Information and Communication Technologies, Bulgarian Academy of Sciences, Sofia, Bulgaria

    Krassimir Georgiev

  4. Sofia University “St. Kliment Ohridski”, Sofia, Bulgaria

    Geno Nikolov

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Hristov, I., Hristova, R., Puzynin, I., Puzynina, T., Sharipov, Z., Tukhliev, Z. (2023). A Database of High Precision Trivial Choreographies for the Planar Three-Body Problem. In: Georgiev, I., Datcheva, M., Georgiev, K., Nikolov, G. (eds) Numerical Methods and Applications. NMA 2022. Lecture Notes in Computer Science, vol 13858. Springer, Cham. https://doi.org/10.1007/978-3-031-32412-3_15

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  • DOI: https://doi.org/10.1007/978-3-031-32412-3_15

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-32411-6

  • Online ISBN: 978-3-031-32412-3

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