Classifying four-body convex central configurations

We classify the full set of convex central configurations in the Newtonian planar four-body problem. Particular attention is given to configurations possessing some type of symmetry or defining geometric property. Special cases considered include kite, trapezoidal, co-circular, equidiagonal, orthodi...

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Vydané v:	Celestial mechanics and dynamical astronomy Ročník 131; číslo 7; s. 1 - 27
Hlavní autori:	Corbera, Montserrat, Cors, Josep M., Roberts, Gareth E.
Médium:	Journal Article Publikácia
Jazyk:	English
Vydavateľské údaje:	Dordrecht Springer Netherlands 01.07.2019 Springer Nature B.V
Predmet:	37 Dynamical systems and ergodic theory 37N Applications 50 years of Celestial Mechanics and Dynamical Astronomy 70 Mechanics of particles and systems 70F Dynamics of a system of particles, including celestial mechanics Aerospace Technology and Astronautics Astrophysics and Astroparticles Central configuration Classical Mechanics Classificació AMS Classification Configurations Convex central configurations Dynamical Systems and Ergodic Theory Enginyeria mecànica Four body problem Geophysics/Geodesy Many-body problem Matemàtiques i estadística n-Body problem Original Article Physics Physics and Astronomy Problema dels cossos múltiples Àrees temàtiques de la UPC Body problem Convex central configurations Central configuration
ISSN:	0923-2958, 1572-9478
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Abstract	We classify the full set of convex central configurations in the Newtonian planar four-body problem. Particular attention is given to configurations possessing some type of symmetry or defining geometric property. Special cases considered include kite, trapezoidal, co-circular, equidiagonal, orthodiagonal, and bisecting-diagonal configurations. Good coordinates for describing the set are established. We use them to prove that the set of four-body convex central configurations with positive masses is three-dimensional, a graph over a domain D that is the union of elementary regions in R + 3 .
AbstractList	We classify the full set of convex central configurations in the Newtonian planar four-body problem. Particular attention is given to configurations possessing some type of symmetry or defining geometric property. Special cases considered include kite, trapezoidal, co-circular, equidiagonal, orthodiagonal, and bisecting-diagonal configurations. Good coordinates for describing the set are established. We use them to prove that the set of four-body convex central configurations with positive masses is three-dimensional, a graph over a domain D that is the union of elementary regions in R + 3 . This is a post-peer-review, pre-copyedit version of an article published in Celestial Mechanics and Dynamical Astronomy. The final authenticated version is available online at: http://dx.doi.org/10.1007/s10569-019-9911-7. We classify the full set of convex central configurations in the Newtonian planar four-body problem. Particular attention is given to configurations possessing some type of symmetry or defining geometric property. Special cases considered include kite, trapezoidal, co-circular, equidiagonal, orthodiagonal, and bisecting-diagonal configurations. Good coordinates for describing the set are established. We use them to prove that the set of four-body convex central configurations with positive masses is three-dimensional, a graph over a domain D that is the union of elementary regions in R+3. Peer Reviewed We classify the full set of convex central configurations in the Newtonian planar four-body problem. Particular attention is given to configurations possessing some type of symmetry or defining geometric property. Special cases considered include kite, trapezoidal, co-circular, equidiagonal, orthodiagonal, and bisecting-diagonal configurations. Good coordinates for describing the set are established. We use them to prove that the set of four-body convex central configurations with positive masses is three-dimensional, a graph over a domain D that is the union of elementary regions in \[{\mathbb {R}}^{+^3}\].
ArticleNumber	34
Author	Cors, Josep M. Roberts, Gareth E. Corbera, Montserrat
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Snippet	We classify the full set of convex central configurations in the Newtonian planar four-body problem. Particular attention is given to configurations possessing... This is a post-peer-review, pre-copyedit version of an article published in Celestial Mechanics and Dynamical Astronomy. The final authenticated version is...
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SubjectTerms	37 Dynamical systems and ergodic theory 37N Applications 50 years of Celestial Mechanics and Dynamical Astronomy 70 Mechanics of particles and systems 70F Dynamics of a system of particles, including celestial mechanics Aerospace Technology and Astronautics Astrophysics and Astroparticles Central configuration Classical Mechanics Classificació AMS Classification Configurations Convex central configurations Dynamical Systems and Ergodic Theory Enginyeria mecànica Four body problem Geophysics/Geodesy Many-body problem Matemàtiques i estadística n-Body problem Original Article Physics Physics and Astronomy Problema dels cossos múltiples Àrees temàtiques de la UPC
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Title	Classifying four-body convex central configurations
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