A Four-Body Convex Central Configuration with Perpendicular Diagonals is Necessarily a Kite
We prove that any four-body convex central configuration with perpendicular diagonals must be a kite configuration. The result extends to general power-law potential functions, including the planar four-vortex problem.
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| Vydané v: | Qualitative theory of dynamical systems Ročník 17; číslo 2; s. 367 - 374 |
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| Hlavní autori: | , , |
| Médium: | Journal Article Publikácia |
| Jazyk: | English |
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Cham
Springer International Publishing
01.07.2018
Springer Nature B.V |
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| ISSN: | 1575-5460, 1662-3592 |
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| Abstract | We prove that any four-body convex central configuration with perpendicular diagonals must be a kite configuration. The result extends to general power-law potential functions, including the planar four-vortex problem. |
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| AbstractList | We prove that any four-body convex central configuration with perpendicular diagonals must be a kite configuration. The result extends to general power-law potential functions, including the planar four-vortex problem. This is a post-peer-review, pre-copyedit version of an article published in Qualitative Theory of Dynamical Systems. The final authenticated version is available online at: http://dx.doi.org/10.1007/s12346-017-0238-z. We prove that any four-body convex central configuration with perpendicular diagonals must be a kite configuration. The result extends to general power-law potential functions, including the planar four-vortex problem. Peer Reviewed |
| Author | Cors, Josep M. Roberts, Gareth E. Corbera, Montserrat |
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| Cites_doi | 10.1007/s10569-012-9431-1 10.1007/s00332-013-9184-3 10.1175/2007MWR2085.1 10.1007/s12346-010-0004-y 10.1088/0951-7715/25/2/343 10.1090/S0273-0979-05-01085-2 10.1007/978-1-4684-9290-3 10.1098/rspa.2007.0320 10.1007/978-3-0348-0933-7_2 |
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| References | Hampton, Roberts, Santoprete (CR6) 2014; 24 CR10 Marsden, Ross (CR8) 2006; 43 Corbera, Delgado, Llibre (CR3) 2009; 8 Albouy, Cabral, Santos (CR1) 2012; 113 Cors, Roberts (CR4) 2012; 25 Davis, Wang, Chen, Chen, Corbosiero, DeMaria, Dudhia, Holland, Klemp, Michalakes, Reeves, Rotunno, Snyder, Xiao (CR5) 2007; 136 CR7 Newton (CR11) 2001 CR9 Albouy, Fu, Sun (CR2) 2008; 464 Schmidt (CR12) 2002 238_CR7 C Davis (238_CR5) 2007; 136 238_CR9 PK Newton (238_CR11) 2001 JM Cors (238_CR4) 2012; 25 238_CR10 JE Marsden (238_CR8) 2006; 43 A Albouy (238_CR2) 2008; 464 A Albouy (238_CR1) 2012; 113 D Schmidt (238_CR12) 2002 M Corbera (238_CR3) 2009; 8 M Hampton (238_CR6) 2014; 24 |
| References_xml | – ident: CR9 – volume: 113 start-page: 369 issue: 4 year: 2012 end-page: 375 ident: CR1 article-title: Some problems on the classical -body problem publication-title: Celest. Mech. Dyn. Astron. doi: 10.1007/s10569-012-9431-1 – year: 2002 ident: CR12 publication-title: Central Configurations and Relative Equilibria for the -Body Problem, Classical and Celestial Mechanics (Recife, 1993/1999) – volume: 24 start-page: 39 year: 2014 end-page: 92 ident: CR6 article-title: Relative equilibria in the four-vortex problem with two pairs of equal vorticities publication-title: J. Nonlinear Sci. doi: 10.1007/s00332-013-9184-3 – volume: 136 start-page: 1990 year: 2007 end-page: 2005 ident: CR5 article-title: Prediction of landfalling hurricanes with the Advanced Hurricane WRF model publication-title: Mon. Weather Rev. doi: 10.1175/2007MWR2085.1 – volume: 8 start-page: 255 issue: 2 year: 2009 end-page: 265 ident: CR3 article-title: On the existence of central configurations of nested -gons publication-title: Qual. Theory Dyn. Syst. doi: 10.1007/s12346-010-0004-y – ident: CR7 – volume: 25 start-page: 343 year: 2012 end-page: 370 ident: CR4 article-title: Four-body co-circular central configurations publication-title: Nonlinearity doi: 10.1088/0951-7715/25/2/343 – volume: 43 start-page: 43 issue: 1 year: 2006 end-page: 73 ident: CR8 article-title: New methods in celestial mechanics and mission design publication-title: Bull. Amer. Math. Soc. (N.S.) doi: 10.1090/S0273-0979-05-01085-2 – year: 2001 ident: CR11 publication-title: The -Vortex Problem: Analytic Techniques doi: 10.1007/978-1-4684-9290-3 – volume: 464 start-page: 1355 issue: 2093 year: 2008 end-page: 1365 ident: CR2 article-title: Symmetry of planar four-body convex central configurations publication-title: Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci. doi: 10.1098/rspa.2007.0320 – ident: CR10 – ident: 238_CR10 doi: 10.1007/978-3-0348-0933-7_2 – volume: 24 start-page: 39 year: 2014 ident: 238_CR6 publication-title: J. Nonlinear Sci. doi: 10.1007/s00332-013-9184-3 – volume-title: The $$N$$-Vortex Problem: Analytic Techniques year: 2001 ident: 238_CR11 doi: 10.1007/978-1-4684-9290-3 – volume: 464 start-page: 1355 issue: 2093 year: 2008 ident: 238_CR2 publication-title: Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci. doi: 10.1098/rspa.2007.0320 – ident: 238_CR7 – ident: 238_CR9 – volume: 8 start-page: 255 issue: 2 year: 2009 ident: 238_CR3 publication-title: Qual. Theory Dyn. Syst. doi: 10.1007/s12346-010-0004-y – volume: 43 start-page: 43 issue: 1 year: 2006 ident: 238_CR8 publication-title: Bull. Amer. Math. Soc. (N.S.) doi: 10.1090/S0273-0979-05-01085-2 – volume-title: Central Configurations and Relative Equilibria for the $$n$$-Body Problem, Classical and Celestial Mechanics (Recife, 1993/1999) year: 2002 ident: 238_CR12 – volume: 25 start-page: 343 year: 2012 ident: 238_CR4 publication-title: Nonlinearity doi: 10.1088/0951-7715/25/2/343 – volume: 113 start-page: 369 issue: 4 year: 2012 ident: 238_CR1 publication-title: Celest. Mech. Dyn. Astron. doi: 10.1007/s10569-012-9431-1 – volume: 136 start-page: 1990 year: 2007 ident: 238_CR5 publication-title: Mon. Weather Rev. doi: 10.1175/2007MWR2085.1 |
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| Title | A Four-Body Convex Central Configuration with Perpendicular Diagonals is Necessarily a Kite |
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