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Linear Stability of the n-gon Relative Equilibria of the (1+n)-Body Problem
Xu, Xingbo1,2,3
2013-04-01
Source PublicationQUALITATIVE THEORY OF DYNAMICAL SYSTEMS
Volume12Issue:1Pages:255-271
AbstractWe consider the linear stability of the regular n-gon relative equilibria of the (1 + n)-body problem. It is shown that there exist at most two kinds of infinitesimal bodies arranged alternatively at the vertices of a regular n-gon when n is even, and only one set of identical infinitesimal bodies when n is odd. In the case of n even, the regular n-gon relative equilibrium is shown to be linearly stable when n >= 14. In each case of n = 8, 10 and 12, linear stability can also be preserved if the ratio of two kinds of masses belongs to an open interval. When n is odd, the related conclusion on the linear stability is recalled.
Keyword(1+n)-body Linear Stability Relative Equilibrium
WOS HeadingsScience & Technology ; Physical Sciences
DOI10.1007/s12346-012-0089-6
WOS KeywordCENTRAL CONFIGURATIONS ; SATELLITES ; SYSTEMS ; RINGS
Indexed BySCI
Language英语
WOS Research AreaMathematics
WOS SubjectMathematics, Applied ; Mathematics
WOS IDWOS:000330801500016
Citation statistics
Document Type期刊论文
Identifierhttp://libir.pmo.ac.cn/handle/332002/15517
Collection太阳和太阳系等离子体研究团组
Affiliation1.Chinese Acad Sci, Purple Mt Observ, Nanjing 210008, Jiangsu, Peoples R China
2.Chinese Acad Sci, Grad Univ, Beijing 100039, Peoples R China
3.Observ Paris, CNRS UMR 8028, F-75014 Paris, France
Recommended Citation
GB/T 7714
Xu, Xingbo. Linear Stability of the n-gon Relative Equilibria of the (1+n)-Body Problem[J]. QUALITATIVE THEORY OF DYNAMICAL SYSTEMS,2013,12(1):255-271.
APA Xu, Xingbo.(2013).Linear Stability of the n-gon Relative Equilibria of the (1+n)-Body Problem.QUALITATIVE THEORY OF DYNAMICAL SYSTEMS,12(1),255-271.
MLA Xu, Xingbo."Linear Stability of the n-gon Relative Equilibria of the (1+n)-Body Problem".QUALITATIVE THEORY OF DYNAMICAL SYSTEMS 12.1(2013):255-271.
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