Dmitrašinović, V, Hudomal, A orcid.org/0000-0002-2782-2675, Shibayama, M et al. (1 more author) (2018) Linear stability of periodic three-body orbits with zero angular momentum and topological dependence of Kepler's third law: a numerical test. Journal of Physics A: Mathematical and Theoretical, 51 (31). 315101. ISSN 1751-8113
Abstract
We test numerically the recently proposed linear relationship between the
scale-invariant period Ts.i. = T|E| 3/2, and the topology of an orbit, on several hundred planar Newtonian periodic three-body orbits. Here T is the period of an orbit, E is its energy, so that Ts.i. is the scale-invariant period, or, equivalently, the period at unit energy |E| = 1. All of these orbits have vanishing angular momentum and pass through a linear, equidistant configuration at least once. Such orbits are classified in ten algebraically well-defined sequences. Orbits in each sequence follow an approximate linear dependence of Ts.i., albeit with slightly different slopes and intercepts. The orbit with the shortest period in its sequence is called the ‘progenitor’: six distinct orbits are the progenitors of these ten sequences. We have studied linear stability of these orbits, with the result that 21 orbits are linearly stable, which includes all of the progenitors. This is consistent with the Birkhoff–Lewis theorem, which implies existence of infinitely many periodic orbits for each stable progenitor, and in this way explains the existence and ensures infinite extension of each sequence.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2018 IOP Publishing Ltd. This is an author-created, un-copyedited version of an article published in Journal of Physics A: Mathematical and Theoretical. IOP Publishing Ltd is not responsible for any errors or omissions in this version of the manuscript or any version derived from it. The Version of Record is available online at https://doi.org/10.1088/1751-8121/aaca41 |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Physics and Astronomy (Leeds) > Theoretical Physics (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 14 Jul 2021 09:00 |
Last Modified: | 14 Jul 2021 09:00 |
Status: | Published |
Publisher: | IOP Publishing |
Identification Number: | 10.1088/1751-8121/aaca41 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:176021 |