Convexity and symmetry of central configurations in the five-body problem: Lagrange plus two
We study convexity and symmetry of central configurations in the five body problem when three of the masses ara located at the vertices of an equilateral triangle, that we call Lagrange plus two central configurations . First, we prove that the two bodies out of the vertices of the triangle cannot b...
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| Veröffentlicht in: | Qualitative theory of dynamical systems 2021-11, Vol.20 (3), Article 63 |
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| container_title | Qualitative theory of dynamical systems |
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| creator | Barrabés, E. Cors, J. M. Fernandes, A. C. Vidal, C. |
| description | We study convexity and symmetry of central configurations in the five body problem when three of the masses ara located at the vertices of an equilateral triangle, that we call
Lagrange plus two central configurations
. First, we prove that the two bodies out of the vertices of the triangle cannot be placed on certain lines. Next, we give a geometrical characterization of such configurations in the sense as that of Dziobek, and we describe the admissible regions where the two remaining bodies can be placed. Furthermore, we prove that any Lagrange plus two central configuration is concave. Finally, we show numerically the existence of non-symmetric central configurations of the five body problem. |
| doi_str_mv | 10.1007/s12346-021-00504-7 |
| format | Article |
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Lagrange plus two central configurations
. First, we prove that the two bodies out of the vertices of the triangle cannot be placed on certain lines. Next, we give a geometrical characterization of such configurations in the sense as that of Dziobek, and we describe the admissible regions where the two remaining bodies can be placed. Furthermore, we prove that any Lagrange plus two central configuration is concave. Finally, we show numerically the existence of non-symmetric central configurations of the five body problem.</description><identifier>ISSN: 1575-5460</identifier><identifier>EISSN: 1662-3592</identifier><identifier>DOI: 10.1007/s12346-021-00504-7</identifier><language>eng</language><publisher>Cham: Springer International Publishing</publisher><subject>Apexes ; Chaos theory ; Configurations ; Convexity ; Difference and Functional Equations ; Dynamical Systems and Ergodic Theory ; Mathematics ; Mathematics and Statistics ; Mathematics, Applied ; Physical Sciences ; Science & Technology ; Symmetry ; Triangles</subject><ispartof>Qualitative theory of dynamical systems, 2021-11, Vol.20 (3), Article 63</ispartof><rights>The Author(s), under exclusive licence to Springer Nature Switzerland AG 2021</rights><rights>The Author(s), under exclusive licence to Springer Nature Switzerland AG 2021.</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>true</woscitedreferencessubscribed><woscitedreferencescount>0</woscitedreferencescount><woscitedreferencesoriginalsourcerecordid>wos000671642000001</woscitedreferencesoriginalsourcerecordid><cites>FETCH-LOGICAL-c314t-c34b1f7c0a5a41cba999e07f4d8393b5182c071c70aad0801398cae3832a62543</cites><orcidid>0000-0001-9297-5101</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/s12346-021-00504-7$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s12346-021-00504-7$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>315,781,785,27929,27930,39263,41493,42562,51324</link.rule.ids></links><search><creatorcontrib>Barrabés, E.</creatorcontrib><creatorcontrib>Cors, J. M.</creatorcontrib><creatorcontrib>Fernandes, A. C.</creatorcontrib><creatorcontrib>Vidal, C.</creatorcontrib><title>Convexity and symmetry of central configurations in the five-body problem: Lagrange plus two</title><title>Qualitative theory of dynamical systems</title><addtitle>Qual. Theory Dyn. Syst</addtitle><addtitle>QUAL THEOR DYN SYST</addtitle><description>We study convexity and symmetry of central configurations in the five body problem when three of the masses ara located at the vertices of an equilateral triangle, that we call
Lagrange plus two central configurations
. First, we prove that the two bodies out of the vertices of the triangle cannot be placed on certain lines. Next, we give a geometrical characterization of such configurations in the sense as that of Dziobek, and we describe the admissible regions where the two remaining bodies can be placed. Furthermore, we prove that any Lagrange plus two central configuration is concave. Finally, we show numerically the existence of non-symmetric central configurations of the five body problem.</description><subject>Apexes</subject><subject>Chaos theory</subject><subject>Configurations</subject><subject>Convexity</subject><subject>Difference and Functional Equations</subject><subject>Dynamical Systems and Ergodic Theory</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Mathematics, Applied</subject><subject>Physical Sciences</subject><subject>Science & Technology</subject><subject>Symmetry</subject><subject>Triangles</subject><issn>1575-5460</issn><issn>1662-3592</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2021</creationdate><recordtype>article</recordtype><sourceid>HGBXW</sourceid><recordid>eNqNkMtKxDAUhosoeH0BVwGXUj25t-6keIMBN7oTQppJx8pMMiap2rc3Y0V3YhbJWXx_zjlfURxjOMMA8jxiQpkogeASgAMr5Vaxh4UgJeU12c41l7zkTMBusR_jC4AgkpK94qnx7s1-9GlE2s1RHFcrm8KIfIeMdSnoJTLedf1iCDr13kXUO5SeLer6N1u2fj6idfDt0q4u0EwvgnYLi9bLIaL07g-LnU4voz36fg-Kx-urh-a2nN3f3DWXs9JQzFK-WYs7aUBzzbBpdV3XFmTH5hWtactxRQxIbCRoPYcKMK0roy2tKNGCcEYPipPp3zzK62BjUi9-CC63VITzLITXQmSKTJQJPsZgO7UO_UqHUWFQG4tqsqiyRfVlUckcOp1C77b1XTS9dcb-BCF7lFgwApuDM139n2769KW08YNLOUqnaMx4lhh-d_hjvE-hs5Wk</recordid><startdate>20211101</startdate><enddate>20211101</enddate><creator>Barrabés, E.</creator><creator>Cors, J. M.</creator><creator>Fernandes, A. C.</creator><creator>Vidal, C.</creator><general>Springer International Publishing</general><general>Springer Nature</general><general>Springer Nature B.V</general><scope>BLEPL</scope><scope>DTL</scope><scope>HGBXW</scope><scope>AAYXX</scope><scope>CITATION</scope><orcidid>https://orcid.org/0000-0001-9297-5101</orcidid></search><sort><creationdate>20211101</creationdate><title>Convexity and symmetry of central configurations in the five-body problem: Lagrange plus two</title><author>Barrabés, E. ; Cors, J. M. ; Fernandes, A. C. ; Vidal, C.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c314t-c34b1f7c0a5a41cba999e07f4d8393b5182c071c70aad0801398cae3832a62543</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2021</creationdate><topic>Apexes</topic><topic>Chaos theory</topic><topic>Configurations</topic><topic>Convexity</topic><topic>Difference and Functional Equations</topic><topic>Dynamical Systems and Ergodic Theory</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Mathematics, Applied</topic><topic>Physical Sciences</topic><topic>Science & Technology</topic><topic>Symmetry</topic><topic>Triangles</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Barrabés, E.</creatorcontrib><creatorcontrib>Cors, J. M.</creatorcontrib><creatorcontrib>Fernandes, A. C.</creatorcontrib><creatorcontrib>Vidal, C.</creatorcontrib><collection>Web of Science Core Collection</collection><collection>Science Citation Index Expanded</collection><collection>Web of Science - Science Citation Index Expanded - 2021</collection><collection>CrossRef</collection><jtitle>Qualitative theory of dynamical systems</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Barrabés, E.</au><au>Cors, J. M.</au><au>Fernandes, A. C.</au><au>Vidal, C.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Convexity and symmetry of central configurations in the five-body problem: Lagrange plus two</atitle><jtitle>Qualitative theory of dynamical systems</jtitle><stitle>Qual. Theory Dyn. Syst</stitle><stitle>QUAL THEOR DYN SYST</stitle><date>2021-11-01</date><risdate>2021</risdate><volume>20</volume><issue>3</issue><artnum>63</artnum><issn>1575-5460</issn><eissn>1662-3592</eissn><abstract>We study convexity and symmetry of central configurations in the five body problem when three of the masses ara located at the vertices of an equilateral triangle, that we call
Lagrange plus two central configurations
. First, we prove that the two bodies out of the vertices of the triangle cannot be placed on certain lines. Next, we give a geometrical characterization of such configurations in the sense as that of Dziobek, and we describe the admissible regions where the two remaining bodies can be placed. Furthermore, we prove that any Lagrange plus two central configuration is concave. Finally, we show numerically the existence of non-symmetric central configurations of the five body problem.</abstract><cop>Cham</cop><pub>Springer International Publishing</pub><doi>10.1007/s12346-021-00504-7</doi><tpages>19</tpages><orcidid>https://orcid.org/0000-0001-9297-5101</orcidid><oa>free_for_read</oa></addata></record> |
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| source | Web of Science - Science Citation Index Expanded - 2021<img src="https://exlibris-pub.s3.amazonaws.com/fromwos-v2.jpg" />; SpringerNature Journals |
| subjects | Apexes Chaos theory Configurations Convexity Difference and Functional Equations Dynamical Systems and Ergodic Theory Mathematics Mathematics and Statistics Mathematics, Applied Physical Sciences Science & Technology Symmetry Triangles |
| title | Convexity and symmetry of central configurations in the five-body problem: Lagrange plus two |
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