{"title":"On Oscillations in a Neighborhood of Lagrangian Libration Points in One\nResonance Case","authors":"Anatoly P. Markeev","doi":"10.1134/S1560354725040136","DOIUrl":null,"url":null,"abstract":"<div><p>This paper addresses the spatial restricted elliptic problem\nof three bodies (material points) gravitating toward each other under Newton’s law of\ngravitation. The eccentricity of the orbit of the main attracting bodies is assumed to be\nsmall, and nonlinear oscillations of\na passively gravitating body near a Lagrangian triangular libration point are studied.\nIt is assumed that in the limiting case of the circular problem the ratio\nof the frequency of rotation of the main bodies about their common center of mass\nto the value of one of the frequencies of small linear oscillations of the passive body\nis exactly equal to three. A detailed analysis is made of two different particular cases of\ninfluence of the three-dimensionality of the\nproblem on the characteristics of nonlinear oscillations of the passive body.</p></div>","PeriodicalId":752,"journal":{"name":"Regular and Chaotic Dynamics","volume":"30 Editors:","pages":"666 - 676"},"PeriodicalIF":0.8000,"publicationDate":"2025-08-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Regular and Chaotic Dynamics","FirstCategoryId":"4","ListUrlMain":"https://link.springer.com/article/10.1134/S1560354725040136","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 0
Abstract
This paper addresses the spatial restricted elliptic problem
of three bodies (material points) gravitating toward each other under Newton’s law of
gravitation. The eccentricity of the orbit of the main attracting bodies is assumed to be
small, and nonlinear oscillations of
a passively gravitating body near a Lagrangian triangular libration point are studied.
It is assumed that in the limiting case of the circular problem the ratio
of the frequency of rotation of the main bodies about their common center of mass
to the value of one of the frequencies of small linear oscillations of the passive body
is exactly equal to three. A detailed analysis is made of two different particular cases of
influence of the three-dimensionality of the
problem on the characteristics of nonlinear oscillations of the passive body.
期刊介绍：
Regular and Chaotic Dynamics (RCD) is an international journal publishing original research papers in dynamical systems theory and its applications. Rooted in the Moscow school of mathematics and mechanics, the journal successfully combines classical problems, modern mathematical techniques and breakthroughs in the field. Regular and Chaotic Dynamics welcomes papers that establish original results, characterized by rigorous mathematical settings and proofs, and that also address practical problems. In addition to research papers, the journal publishes review articles, historical and polemical essays, and translations of works by influential scientists of past centuries, previously unavailable in English. Along with regular issues, RCD also publishes special issues devoted to particular topics and events in the world of dynamical systems.
求助内容：
应助结果提醒方式：
京公网安备 11010802042870号
