An efficient approach for searching three-body periodic orbits passing through Eulerian configuration

IF 1.9 4区 物理与天体物理 Q2 ASTRONOMY & ASTROPHYSICS
I. Hristov, R. Hristova
{"title":"An efficient approach for searching three-body periodic orbits passing through Eulerian configuration","authors":"I. Hristov,&nbsp;R. Hristova","doi":"10.1016/j.ascom.2024.100880","DOIUrl":null,"url":null,"abstract":"<div><div>A new efficient approach for searching three-body periodic equal-mass collisionless orbits passing through Eulerian configuration is presented. The approach is based on a symmetry property of the solutions at the half period. Depending on two previously established symmetry types on the shape sphere, each solution is presented by one or two distinct initial conditions (one or two points in the search domain). A numerical search based on Newton’s method on a relatively coarse search grid for solutions with relatively small scale-invariant periods <span><math><mrow><msup><mrow><mi>T</mi></mrow><mrow><mo>∗</mo></mrow></msup><mo>&lt;</mo><mn>70</mn></mrow></math></span> is conducted. The linear systems at each Newton’s iteration are computed by high order high precision Taylor series method. The search produced 12,431 initial conditions (i.c.s) corresponding to 6333 distinct solutions. In addition to passing through the Eulerian configuration, 35 of the solutions are also free-fall ones. Although most of the found solutions are new, all linearly stable solutions among them (only 7) are old ones. Particular attention is paid to the details of the high precision computations and the analysis of accuracy. All i.c.s are given with 100 correct digits.</div></div>","PeriodicalId":48757,"journal":{"name":"Astronomy and Computing","volume":"49 ","pages":"Article 100880"},"PeriodicalIF":1.9000,"publicationDate":"2024-09-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S2213133724000957/pdfft?md5=e0e9ef0e698ea1e1adc33a7e5eff7275&pid=1-s2.0-S2213133724000957-main.pdf","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Astronomy and Computing","FirstCategoryId":"101","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S2213133724000957","RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"ASTRONOMY & ASTROPHYSICS","Score":null,"Total":0}
引用次数: 0

Abstract

A new efficient approach for searching three-body periodic equal-mass collisionless orbits passing through Eulerian configuration is presented. The approach is based on a symmetry property of the solutions at the half period. Depending on two previously established symmetry types on the shape sphere, each solution is presented by one or two distinct initial conditions (one or two points in the search domain). A numerical search based on Newton’s method on a relatively coarse search grid for solutions with relatively small scale-invariant periods T<70 is conducted. The linear systems at each Newton’s iteration are computed by high order high precision Taylor series method. The search produced 12,431 initial conditions (i.c.s) corresponding to 6333 distinct solutions. In addition to passing through the Eulerian configuration, 35 of the solutions are also free-fall ones. Although most of the found solutions are new, all linearly stable solutions among them (only 7) are old ones. Particular attention is paid to the details of the high precision computations and the analysis of accuracy. All i.c.s are given with 100 correct digits.
搜索通过欧拉构型的三体周期轨道的有效方法
本文提出了一种新的高效方法,用于搜索通过欧拉构型的三体周期性等质量无碰撞轨道。该方法基于半周期解的对称性。根据先前在形状球上建立的两种对称类型,每个解由一个或两个不同的初始条件(搜索域中的一个或两个点)呈现。基于牛顿法,在相对较粗的搜索网格上对具有相对较小的尺度不变周期 T∗<70 的解进行数值搜索。每次牛顿迭代的线性系统都是通过高阶高精度泰勒级数法计算得出的。搜索产生了 12,431 个初始条件(i.c.s),对应于 6333 个不同的解。除了通过欧拉构型外,其中 35 个解也是自由落体解。虽然找到的解大多是新解,但其中所有线性稳定解(只有 7 个)都是旧解。我们特别关注高精度计算的细节和精度分析。所有 i.c.s 都给出了 100 位正确数字。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
求助全文
约1分钟内获得全文 求助全文
来源期刊
Astronomy and Computing
Astronomy and Computing ASTRONOMY & ASTROPHYSICSCOMPUTER SCIENCE,-COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS
CiteScore
4.10
自引率
8.00%
发文量
67
期刊介绍: Astronomy and Computing is a peer-reviewed journal that focuses on the broad area between astronomy, computer science and information technology. The journal aims to publish the work of scientists and (software) engineers in all aspects of astronomical computing, including the collection, analysis, reduction, visualisation, preservation and dissemination of data, and the development of astronomical software and simulations. The journal covers applications for academic computer science techniques to astronomy, as well as novel applications of information technologies within astronomy.
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
确定
请完成安全验证×
copy
已复制链接
快去分享给好友吧!
我知道了
右上角分享
点击右上角分享
0
联系我们:info@booksci.cn Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术官方微信