On Strictly Convex Central Configurations of the 2n-Body Problem
We consider planar central configurations of the Newtonian 2 n -body problem consisting in two twisted regular n -gons of equal masses. We prove the conjecture that for n ≥ 5 all convex central configurations of two twisted regular n -gons are strictly convex.
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| Published in: | Journal of dynamics and differential equations Vol. 31; no. 4; pp. 2293 - 2304 |
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| Main Authors: | , |
| Format: | Journal Article Publication |
| Language: | English |
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01.12.2019
Springer Nature B.V |
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| ISSN: | 1040-7294, 1572-9222 |
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| Abstract | We consider planar central configurations of the Newtonian 2
n
-body problem consisting in two twisted regular
n
-gons of equal masses. We prove the conjecture that for
n
≥
5
all convex central configurations of two twisted regular
n
-gons are strictly convex. |
|---|---|
| AbstractList | We consider planar central configurations of the Newtonian 2
n
-body problem consisting in two twisted regular
n
-gons of equal masses. We prove the conjecture that for
n
≥
5
all convex central configurations of two twisted regular
n
-gons are strictly convex. We consider planar central configurations of the Newtonian 2n-body problem consisting in two twisted regular n-gons of equal masses. We prove the conjecture that for n≥5 all convex central configurations of two twisted regular n-gons are strictly convex. We consider planar central configurations of the Newtonian 2n-body problem consisting in two twisted regular n-gons of equal masses. We prove the conjecture that for n=5 all convex central configurations of two twisted regular n-gons are strictly convex. Peer Reviewed |
| Author | Cors, J. M. Barrabés, E. |
| Author_xml | – sequence: 1 givenname: E. orcidid: 0000-0002-8448-692X surname: Barrabés fullname: Barrabés, E. email: esther.barrabes@udg.edu organization: Escola Politècnica Superior, Universitat de Girona – sequence: 2 givenname: J. M. orcidid: 0000-0002-9803-8490 surname: Cors fullname: Cors, J. M. organization: Escola Politècnica Superior d’Enginyeria de Manresa, Universitat Politècnica de Catalunya |
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| Cites_doi | 10.1007/s10884-017-9596-0 10.1016/j.jde.2012.06.017 10.1007/s10884-011-9233-2 10.1007/978-3-319-22129-8_3 10.1142/9789812792617_0006 10.1090/cbms/104 |
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| Contributor | Universitat Politècnica de Catalunya. Departament de Matemàtiques |
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| Keywords | Body problem Twisted central configuration 70F10 Central configuration 70F15 Convex central configuration |
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| References | YuXZhangSTwisted angles for central configurations formed by two twisted regular polygonsJ. Differ. Equ.201225321062122294696510.1016/j.jde.2012.06.017 Barrabés, E., Cors, J.: On central configurations of twisted crowns. arXiv:1612.07135 (2016) ChenKCHsiaoJSConvex central configurations of the n\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$n$$\end{document}-body problem which are not strictly convexJ. Dyn. Differ. Equ.201224119128289034010.1007/s10884-011-9233-2 Saari, D.G.: Collisions, rings, and other Newtonian N\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$N$$\end{document}-body problems, CBMS Regional Conference Series in Mathematics, vol 104. Published for the Conference Board of the Mathematical Sciences, Washington, DC; by the American Mathematical Society, Providence, RI (2005) FernandesAGarciaBMelloLConvex but not strictly convex central configurationsJ. Dyn. Differ. Equ.201710.1007/s10884-017-9596-006973959 Roberts, G.: Existence and stability of relative equilibria in the n-body problem. PhD thesis, Boston University (1999) X Yu (9708_CR6) 2012; 253 KC Chen (9708_CR2) 2012; 24 9708_CR1 A Fernandes (9708_CR3) 2017 9708_CR5 9708_CR4 |
| References_xml | – reference: FernandesAGarciaBMelloLConvex but not strictly convex central configurationsJ. Dyn. Differ. Equ.201710.1007/s10884-017-9596-006973959 – reference: Barrabés, E., Cors, J.: On central configurations of twisted crowns. arXiv:1612.07135 (2016) – reference: ChenKCHsiaoJSConvex central configurations of the n\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$n$$\end{document}-body problem which are not strictly convexJ. Dyn. Differ. Equ.201224119128289034010.1007/s10884-011-9233-2 – reference: Saari, D.G.: Collisions, rings, and other Newtonian N\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$N$$\end{document}-body problems, CBMS Regional Conference Series in Mathematics, vol 104. Published for the Conference Board of the Mathematical Sciences, Washington, DC; by the American Mathematical Society, Providence, RI (2005) – reference: YuXZhangSTwisted angles for central configurations formed by two twisted regular polygonsJ. Differ. Equ.201225321062122294696510.1016/j.jde.2012.06.017 – reference: Roberts, G.: Existence and stability of relative equilibria in the n-body problem. PhD thesis, Boston University (1999) – year: 2017 ident: 9708_CR3 publication-title: J. Dyn. Differ. Equ. doi: 10.1007/s10884-017-9596-0 – volume: 253 start-page: 2106 year: 2012 ident: 9708_CR6 publication-title: J. Differ. Equ. doi: 10.1016/j.jde.2012.06.017 – volume: 24 start-page: 119 year: 2012 ident: 9708_CR2 publication-title: J. Dyn. Differ. Equ. doi: 10.1007/s10884-011-9233-2 – ident: 9708_CR1 doi: 10.1007/978-3-319-22129-8_3 – ident: 9708_CR4 doi: 10.1142/9789812792617_0006 – ident: 9708_CR5 doi: 10.1090/cbms/104 |
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| Snippet | We consider planar central configurations of the Newtonian 2
n
-body problem consisting in two twisted regular
n
-gons of equal masses. We prove the conjecture... We consider planar central configurations of the Newtonian 2n-body problem consisting in two twisted regular n-gons of equal masses. We prove the conjecture... |
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| SubjectTerms | 70 Mechanics of particles and systems 70F Dynamics of a system of particles, including celestial mechanics Applications of Mathematics Central configuration Classificació AMS Configurations Convex central configuration Many-body problem Matemàtiques i estadística Mathematics Mathematics and Statistics n-Body problem Ordinary Differential Equations Partial Differential Equations Problema dels cossos múltiples Twisted central configuration Àrees temàtiques de la UPC |
| Title | On Strictly Convex Central Configurations of the 2n-Body Problem |
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