Hill stability of the coplanar four-body problem with a binary subsystem
Abstract We consider a coplanar four-body system including a binary subsystem. The Hill stability is studied using the zero velocity surface of the four-body problem. The value of c 2 E determines the topology of zero-velocity surfaces and hence regions of possible motions that bifurcates at the col...
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| Veröffentlicht in: | Monthly notices of the Royal Astronomical Society 2017-08, Vol.469 (3), p.3576-3587 |
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| container_issue | 3 |
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| container_title | Monthly notices of the Royal Astronomical Society |
| container_volume | 469 |
| creator | Liu, Chao Gong, Shengping |
| description | Abstract
We consider
a coplanar four-body system including a binary subsystem. The Hill stability is studied using the zero velocity surface of the four-body problem. The value of c
2
E determines the topology of zero-velocity surfaces and hence regions of possible motions that bifurcates at the collinear equilibrium points. The Hill stability of the system is determined by the relation between the actual and critical values of c
2
E. The critical value of c
2
E is determined by the mass of the bodies and other two time-varying parameters associated to the orbit of binary. The influences of the two parameters on the Hill stability are investigated and discussed. Different from the three-body problem, the primary bifurcation may happen at different equilibrium points. Besides, a new temporary Hill stability is defined to illustrate the case that the system may be stable or unstable. |
| doi_str_mv | 10.1093/mnras/stx1017 |
| format | Article |
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We consider
a coplanar four-body system including a binary subsystem. The Hill stability is studied using the zero velocity surface of the four-body problem. The value of c
2
E determines the topology of zero-velocity surfaces and hence regions of possible motions that bifurcates at the collinear equilibrium points. The Hill stability of the system is determined by the relation between the actual and critical values of c
2
E. The critical value of c
2
E is determined by the mass of the bodies and other two time-varying parameters associated to the orbit of binary. The influences of the two parameters on the Hill stability are investigated and discussed. Different from the three-body problem, the primary bifurcation may happen at different equilibrium points. Besides, a new temporary Hill stability is defined to illustrate the case that the system may be stable or unstable.</description><identifier>ISSN: 0035-8711</identifier><identifier>EISSN: 1365-2966</identifier><identifier>DOI: 10.1093/mnras/stx1017</identifier><language>eng</language><publisher>Oxford University Press</publisher><ispartof>Monthly notices of the Royal Astronomical Society, 2017-08, Vol.469 (3), p.3576-3587</ispartof><rights>2017 The Authors Published by Oxford University Press on behalf of the Royal Astronomical Society 2017</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c270t-7641e22eb6f3cd3d17460d777971752cf4ad1ed2b80596e64304305dd84429293</citedby><cites>FETCH-LOGICAL-c270t-7641e22eb6f3cd3d17460d777971752cf4ad1ed2b80596e64304305dd84429293</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>314,780,784,1603,27923,27924</link.rule.ids><linktorsrc>$$Uhttps://dx.doi.org/10.1093/mnras/stx1017$$EView_record_in_Oxford_University_Press$$FView_record_in_$$GOxford_University_Press</linktorsrc></links><search><creatorcontrib>Liu, Chao</creatorcontrib><creatorcontrib>Gong, Shengping</creatorcontrib><title>Hill stability of the coplanar four-body problem with a binary subsystem</title><title>Monthly notices of the Royal Astronomical Society</title><description>Abstract
We consider
a coplanar four-body system including a binary subsystem. The Hill stability is studied using the zero velocity surface of the four-body problem. The value of c
2
E determines the topology of zero-velocity surfaces and hence regions of possible motions that bifurcates at the collinear equilibrium points. The Hill stability of the system is determined by the relation between the actual and critical values of c
2
E. The critical value of c
2
E is determined by the mass of the bodies and other two time-varying parameters associated to the orbit of binary. The influences of the two parameters on the Hill stability are investigated and discussed. Different from the three-body problem, the primary bifurcation may happen at different equilibrium points. Besides, a new temporary Hill stability is defined to illustrate the case that the system may be stable or unstable.</description><issn>0035-8711</issn><issn>1365-2966</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2017</creationdate><recordtype>article</recordtype><recordid>eNqFkD1PwzAYhC0EEqUwsntkMX39ETseUQUEqRILzJEdO2pQUke2I8i_J9DunW64R6fTg9A9hUcKmm-GQzRpk_IPBaou0IpyWRCmpbxEKwBekFJReo1uUvoCAMGZXKGq6voep2xs13d5xqHFee9xE8beHEzEbZgiscHNeIzB9n7A313eY4Ntt9QzTpNNc8p-uEVXremTvzvlGn2-PH9sK7J7f33bPu1IwxRkoqSgnjFvZcsbxx1VQoJTSmlFVcGaVhhHvWO2hEJLLwVfjkLhXCkE00zzNSLH3SaGlKJv6zF2w3KlplD_aaj_NdQnDQv_cOTDNJ5BfwHHIV_4</recordid><startdate>20170811</startdate><enddate>20170811</enddate><creator>Liu, Chao</creator><creator>Gong, Shengping</creator><general>Oxford University Press</general><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>20170811</creationdate><title>Hill stability of the coplanar four-body problem with a binary subsystem</title><author>Liu, Chao ; Gong, Shengping</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c270t-7641e22eb6f3cd3d17460d777971752cf4ad1ed2b80596e64304305dd84429293</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2017</creationdate><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Liu, Chao</creatorcontrib><creatorcontrib>Gong, Shengping</creatorcontrib><collection>CrossRef</collection><jtitle>Monthly notices of the Royal Astronomical Society</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext_linktorsrc</fulltext></delivery><addata><au>Liu, Chao</au><au>Gong, Shengping</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Hill stability of the coplanar four-body problem with a binary subsystem</atitle><jtitle>Monthly notices of the Royal Astronomical Society</jtitle><date>2017-08-11</date><risdate>2017</risdate><volume>469</volume><issue>3</issue><spage>3576</spage><epage>3587</epage><pages>3576-3587</pages><issn>0035-8711</issn><eissn>1365-2966</eissn><abstract>Abstract
We consider
a coplanar four-body system including a binary subsystem. The Hill stability is studied using the zero velocity surface of the four-body problem. The value of c
2
E determines the topology of zero-velocity surfaces and hence regions of possible motions that bifurcates at the collinear equilibrium points. The Hill stability of the system is determined by the relation between the actual and critical values of c
2
E. The critical value of c
2
E is determined by the mass of the bodies and other two time-varying parameters associated to the orbit of binary. The influences of the two parameters on the Hill stability are investigated and discussed. Different from the three-body problem, the primary bifurcation may happen at different equilibrium points. Besides, a new temporary Hill stability is defined to illustrate the case that the system may be stable or unstable.</abstract><pub>Oxford University Press</pub><doi>10.1093/mnras/stx1017</doi><tpages>12</tpages></addata></record> |
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| source | Oxford Journals Open Access Collection |
| title | Hill stability of the coplanar four-body problem with a binary subsystem |
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