{"title":"具有对数引力相互作用的正弦旋转平衡态","authors":"Anna-Monika Muscaş, Daniel Paşca, Cristina Stoica","doi":"10.1007/s10569-024-10185-4","DOIUrl":null,"url":null,"abstract":"<p>We study the linear stability of regular <i>n</i>-gon rotating equilibria in the <i>n</i>-body problem with logarithm interaction. We find that linear stability is insured if a central mass <i>M</i> if <i>M</i> is bounded below and above by constants depending on the number and mass of the (equal) outer <i>n</i> bodies. Moreover, we provide explicit formulae for these bounds. In the absence of a central mass, we find that the regular <i>n</i>-gon is linearly stable for <span>\\(n =2,3,\\ldots 6\\)</span> only.</p>","PeriodicalId":72537,"journal":{"name":"Celestial mechanics and dynamical astronomy","volume":"28 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-04-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Regular n-gon rotating equilibria with logarithm gravitational interaction\",\"authors\":\"Anna-Monika Muscaş, Daniel Paşca, Cristina Stoica\",\"doi\":\"10.1007/s10569-024-10185-4\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>We study the linear stability of regular <i>n</i>-gon rotating equilibria in the <i>n</i>-body problem with logarithm interaction. We find that linear stability is insured if a central mass <i>M</i> if <i>M</i> is bounded below and above by constants depending on the number and mass of the (equal) outer <i>n</i> bodies. Moreover, we provide explicit formulae for these bounds. In the absence of a central mass, we find that the regular <i>n</i>-gon is linearly stable for <span>\\\\(n =2,3,\\\\ldots 6\\\\)</span> only.</p>\",\"PeriodicalId\":72537,\"journal\":{\"name\":\"Celestial mechanics and dynamical astronomy\",\"volume\":\"28 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-04-18\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Celestial mechanics and dynamical astronomy\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1007/s10569-024-10185-4\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Celestial mechanics and dynamical astronomy","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1007/s10569-024-10185-4","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
摘要
我们研究了具有对数交互作用的 n 个体问题中规则 n 离子旋转平衡态的线性稳定性。我们发现，如果中心质量 M 的下方和上方都有常数约束，而这些常数取决于（相等的）n 个外体的数量和质量，那么线性稳定性就会得到保证。此外，我们还为这些界限提供了明确的公式。在没有中心质量的情况下，我们发现正则n-坤仅在\(n =2,3,\ldots 6\) 时是线性稳定的。
Regular n-gon rotating equilibria with logarithm gravitational interaction
We study the linear stability of regular n-gon rotating equilibria in the n-body problem with logarithm interaction. We find that linear stability is insured if a central mass M if M is bounded below and above by constants depending on the number and mass of the (equal) outer n bodies. Moreover, we provide explicit formulae for these bounds. In the absence of a central mass, we find that the regular n-gon is linearly stable for \(n =2,3,\ldots 6\) only.
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