{"title":"Symmetric comet-type periodic orbits in the elliptic three-dimensional restricted (N+1)-body problem","authors":"Josep M. Cors , Miguel Garrido","doi":"10.1016/j.physd.2024.134426","DOIUrl":null,"url":null,"abstract":"<div><div>For <span><math><mrow><mi>N</mi><mo>≥</mo><mn>3</mn></mrow></math></span>, we show the existence of symmetric periodic orbits of very large radii in the elliptic three-dimensional restricted <span><math><mrow><mo>(</mo><mi>N</mi><mo>+</mo><mn>1</mn><mo>)</mo></mrow></math></span>-body problem when the <span><math><mi>N</mi></math></span> primaries have equal masses and are arranged in a <span><math><mi>N</mi></math></span>-gon central configuration. These periodic orbits are close to very large circular Keplerian orbits lying nearly a plane perpendicular to that of the primaries. They exist for a discrete sequence of values of the mean motion, no matter the value of the eccentricity of the primaries.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"470 ","pages":"Article 134426"},"PeriodicalIF":2.7000,"publicationDate":"2024-11-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Physica D: Nonlinear Phenomena","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0167278924003762","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
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Abstract
For , we show the existence of symmetric periodic orbits of very large radii in the elliptic three-dimensional restricted -body problem when the primaries have equal masses and are arranged in a -gon central configuration. These periodic orbits are close to very large circular Keplerian orbits lying nearly a plane perpendicular to that of the primaries. They exist for a discrete sequence of values of the mean motion, no matter the value of the eccentricity of the primaries.
期刊介绍：
Physica D (Nonlinear Phenomena) publishes research and review articles reporting on experimental and theoretical works, techniques and ideas that advance the understanding of nonlinear phenomena. Topics encompass wave motion in physical, chemical and biological systems; physical or biological phenomena governed by nonlinear field equations, including hydrodynamics and turbulence; pattern formation and cooperative phenomena; instability, bifurcations, chaos, and space-time disorder; integrable/Hamiltonian systems; asymptotic analysis and, more generally, mathematical methods for nonlinear systems.
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