{"title":"圆形受限三体问题的三维多时间尺度近似解析解","authors":"F. Gao, Yongqing Wang","doi":"10.1155/2020/8868137","DOIUrl":null,"url":null,"abstract":"We illustrate the chaotic nature of the circular restricted three-body problem from the perspective of the bifurcation diagram with respect to the mass ratio parameter. Moreover, it is shown that when the frequency ratio in different directions of the classical problem is irrational, it has the quasiperiodic characteristics. In addition, a three-dimensional approximate solution to this problem under two time scales is proposed by using the multiple time scales method.","PeriodicalId":48962,"journal":{"name":"Advances in Astronomy","volume":" ","pages":"1-10"},"PeriodicalIF":1.6000,"publicationDate":"2020-11-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":"{\"title\":\"Approximate Analytical Three-Dimensional Multiple Time Scales Solution to a Circular Restricted Three-Body Problem\",\"authors\":\"F. Gao, Yongqing Wang\",\"doi\":\"10.1155/2020/8868137\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We illustrate the chaotic nature of the circular restricted three-body problem from the perspective of the bifurcation diagram with respect to the mass ratio parameter. Moreover, it is shown that when the frequency ratio in different directions of the classical problem is irrational, it has the quasiperiodic characteristics. In addition, a three-dimensional approximate solution to this problem under two time scales is proposed by using the multiple time scales method.\",\"PeriodicalId\":48962,\"journal\":{\"name\":\"Advances in Astronomy\",\"volume\":\" \",\"pages\":\"1-10\"},\"PeriodicalIF\":1.6000,\"publicationDate\":\"2020-11-10\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"2\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Advances in Astronomy\",\"FirstCategoryId\":\"101\",\"ListUrlMain\":\"https://doi.org/10.1155/2020/8868137\",\"RegionNum\":4,\"RegionCategory\":\"物理与天体物理\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"ASTRONOMY & ASTROPHYSICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Advances in Astronomy","FirstCategoryId":"101","ListUrlMain":"https://doi.org/10.1155/2020/8868137","RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"ASTRONOMY & ASTROPHYSICS","Score":null,"Total":0}
Approximate Analytical Three-Dimensional Multiple Time Scales Solution to a Circular Restricted Three-Body Problem
We illustrate the chaotic nature of the circular restricted three-body problem from the perspective of the bifurcation diagram with respect to the mass ratio parameter. Moreover, it is shown that when the frequency ratio in different directions of the classical problem is irrational, it has the quasiperiodic characteristics. In addition, a three-dimensional approximate solution to this problem under two time scales is proposed by using the multiple time scales method.
期刊介绍：
Advances in Astronomy publishes articles in all areas of astronomy, astrophysics, and cosmology. The journal accepts both observational and theoretical investigations into celestial objects and the wider universe, as well as the reports of new methods and instrumentation for their study.
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