Linear stability of periodic three-body orbits with zero angular momentum and topological dependence of Kepler’s third law: a numerical test

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dc.citation.issue31
dc.citation.rankM21
dc.citation.spage315101
dc.citation.volume51
dc.contributor.authorDmitrašinović, Veljko
dc.contributor.authorHudomal, Ana
dc.contributor.authorShibayama, Mitsuru
dc.contributor.authorSugita, Ayumu
dc.date.accessioned2024-07-02T08:36:31Z
dc.date.available2024-07-02T08:36:31Z
dc.date.issued2018-06-22
dc.description.abstractWe 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.
dc.identifier.doi10.1088/1751-8121/aaca41
dc.identifier.issn1751-8113
dc.identifier.issn1751-8121
dc.identifier.scopus2-s2.0-85049593640
dc.identifier.urihttps://pub.ipb.ac.rs/handle/123456789/166
dc.identifier.wos000436116400001
dc.language.isoen
dc.publisherInstitute of Physics Publishing
dc.relation.ispartofJournal of Physics A: Mathematical and Theoretical
dc.relation.ispartofabbrJ. Phys. A.
dc.rightsopenAccess
dc.titleLinear stability of periodic three-body orbits with zero angular momentum and topological dependence of Kepler’s third law: a numerical test
dc.typeArticle
dc.type.versionpublishedVersion
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