The Broucke-H\'enon orbit and the Schubart Orbit in the planar three-body problem with equal masses
In this paper, we study the variational properties of two special orbits: the Schubart orbit and the Broucke-H\'{e}non orbit. We show that under an appropriate topological constraint, the action minimizer must be either the Schubart orbit or the Broucke-H\'{e}non orbit. One of the main cha...
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| creator | Kuang, Wentian Ouyang, Tiancheng Xie, Zhifu Yan, Duokui |
| description | In this paper, we study the variational properties of two special orbits: the
Schubart orbit and the Broucke-H\'{e}non orbit. We show that under an
appropriate topological constraint, the action minimizer must be either the
Schubart orbit or the Broucke-H\'{e}non orbit. One of the main challenges is to
prove that the Schubart orbit coincides with the action minimizer connecting a
collinear configuration with a binary collision and an isosceles configuration.
A new geometric argument is introduced to overcome this challenge. |
| doi_str_mv | 10.48550/arxiv.1607.00580 |
| format | Article |
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Schubart orbit and the Broucke-H\'{e}non orbit. We show that under an
appropriate topological constraint, the action minimizer must be either the
Schubart orbit or the Broucke-H\'{e}non orbit. One of the main challenges is to
prove that the Schubart orbit coincides with the action minimizer connecting a
collinear configuration with a binary collision and an isosceles configuration.
A new geometric argument is introduced to overcome this challenge.</description><identifier>DOI: 10.48550/arxiv.1607.00580</identifier><language>eng</language><subject>Mathematics - Dynamical Systems</subject><creationdate>2016-07</creationdate><rights>http://arxiv.org/licenses/nonexclusive-distrib/1.0</rights><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>228,230,780,885</link.rule.ids><linktorsrc>$$Uhttps://arxiv.org/abs/1607.00580$$EView_record_in_Cornell_University$$FView_record_in_$$GCornell_University$$Hfree_for_read</linktorsrc><backlink>$$Uhttps://doi.org/10.48550/arXiv.1607.00580$$DView paper in arXiv$$Hfree_for_read</backlink></links><search><creatorcontrib>Kuang, Wentian</creatorcontrib><creatorcontrib>Ouyang, Tiancheng</creatorcontrib><creatorcontrib>Xie, Zhifu</creatorcontrib><creatorcontrib>Yan, Duokui</creatorcontrib><title>The Broucke-H\'enon orbit and the Schubart Orbit in the planar three-body problem with equal masses</title><description>In this paper, we study the variational properties of two special orbits: the
Schubart orbit and the Broucke-H\'{e}non orbit. We show that under an
appropriate topological constraint, the action minimizer must be either the
Schubart orbit or the Broucke-H\'{e}non orbit. One of the main challenges is to
prove that the Schubart orbit coincides with the action minimizer connecting a
collinear configuration with a binary collision and an isosceles configuration.
A new geometric argument is introduced to overcome this challenge.</description><subject>Mathematics - Dynamical Systems</subject><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2016</creationdate><recordtype>article</recordtype><sourceid>GOX</sourceid><recordid>eNqFjrEOgkAQRK-xMOoHWLmdFXhEUWqNhs5CShOywBouHne4HCp_LxJ7q5m8meIJMQ-kv4nCUK6Q3-rpB1u586UMIzkWeVIS7Nm2-Z28-LokYw1YzpQDNAW4fr3kZZshOzgPWJmB1hoNcl-ZyMts0UHNNtNUwUu5EujRooYKm4aaqRjdUDc0--VELE7H5BB7g05as6qQu_SrlQ5a6_-PD8OkQuY</recordid><startdate>20160702</startdate><enddate>20160702</enddate><creator>Kuang, Wentian</creator><creator>Ouyang, Tiancheng</creator><creator>Xie, Zhifu</creator><creator>Yan, Duokui</creator><scope>AKZ</scope><scope>GOX</scope></search><sort><creationdate>20160702</creationdate><title>The Broucke-H\'enon orbit and the Schubart Orbit in the planar three-body problem with equal masses</title><author>Kuang, Wentian ; Ouyang, Tiancheng ; Xie, Zhifu ; Yan, Duokui</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-arxiv_primary_1607_005803</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2016</creationdate><topic>Mathematics - Dynamical Systems</topic><toplevel>online_resources</toplevel><creatorcontrib>Kuang, Wentian</creatorcontrib><creatorcontrib>Ouyang, Tiancheng</creatorcontrib><creatorcontrib>Xie, Zhifu</creatorcontrib><creatorcontrib>Yan, Duokui</creatorcontrib><collection>arXiv Mathematics</collection><collection>arXiv.org</collection></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext_linktorsrc</fulltext></delivery><addata><au>Kuang, Wentian</au><au>Ouyang, Tiancheng</au><au>Xie, Zhifu</au><au>Yan, Duokui</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>The Broucke-H\'enon orbit and the Schubart Orbit in the planar three-body problem with equal masses</atitle><date>2016-07-02</date><risdate>2016</risdate><abstract>In this paper, we study the variational properties of two special orbits: the
Schubart orbit and the Broucke-H\'{e}non orbit. We show that under an
appropriate topological constraint, the action minimizer must be either the
Schubart orbit or the Broucke-H\'{e}non orbit. One of the main challenges is to
prove that the Schubart orbit coincides with the action minimizer connecting a
collinear configuration with a binary collision and an isosceles configuration.
A new geometric argument is introduced to overcome this challenge.</abstract><doi>10.48550/arxiv.1607.00580</doi><oa>free_for_read</oa></addata></record> |
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| subjects | Mathematics - Dynamical Systems |
| title | The Broucke-H\'enon orbit and the Schubart Orbit in the planar three-body problem with equal masses |
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