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The family of planar periodic orbits generated by the equal-mass four-body Schubart interplay orbit

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Abstract

We locate members of a one-parameter family of equal-mass four-body periodic orbits in the plane. The family begins and ends with the rectilinear four-body equal-mass Schubart interplay orbit and passes through a double choreography orbit. The first-order stability of these orbits is computed. Some members of this symmetric family are stable to symmetric perturbations; however, they are unstable when all perturbations are allowed.

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Acknowledgements

Valerie Chopovda is grateful to Massey University for funding to support this study. Valerie Chopovda is also grateful to the New Zealand Mathematical Society for the Gloria Olive Travel Grant that helped fund her participation in the CELMEC VII conference. Winston Sweatman is grateful for the hospitality of Professor Bonnie Steves and Glasgow Caledonian University during a number of visits.

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  1. Massey University, Auckland, New Zealand

    Valerie Chopovda & Winston L. Sweatman

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  1. Valerie Chopovda
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  2. Winston L. Sweatman
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Correspondence to Valerie Chopovda.

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This article is part of the topical collection on Recent advances in the study of the dynamics of N-body problem.

Guest Editors: Giovanni Federico Gronchi, Ugo Locatelli, Giuseppe Pucacco and Alessandra Celletti.

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Chopovda, V., Sweatman, W.L. The family of planar periodic orbits generated by the equal-mass four-body Schubart interplay orbit. Celest Mech Dyn Astr 130, 39 (2018). https://doi.org/10.1007/s10569-018-9831-y

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  • DOI: https://doi.org/10.1007/s10569-018-9831-y

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