Trapezoid central configurations
We classify all planar four–body central configurations where two pairs of the bodies are on parallel lines. Using cartesian coordinates, we show that the set of four–body trapezoid central configurations with positive masses forms a two–dimensional surface where two symmetric families, the rhombus...
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| Vydané v: | Applied mathematics and computation Ročník 346; s. 127 - 142 |
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01.04.2019
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| Abstract | We classify all planar four–body central configurations where two pairs of the bodies are on parallel lines. Using cartesian coordinates, we show that the set of four–body trapezoid central configurations with positive masses forms a two–dimensional surface where two symmetric families, the rhombus and isosceles trapezoid, are on its boundary. We also prove that, for a given position of the bodies, in some cases a specific order of the masses determines the geometry of the configuration, namely acute or obtuse trapezoid central configuration. We also prove the existence of non–symmetric trapezoid central configurations with two pairs of equal masses. |
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| AbstractList | We classify all planar four–body central configurations where two pairs of the bodies are on parallel lines. Using cartesian coordinates, we show that the set of four–body trapezoid central configurations with positive masses forms a two–dimensional surface where two symmetric families, the rhombus and isosceles trapezoid, are on its boundary. We also prove that, for a given position of the bodies, in some cases a specific order of the masses determines the geometry of the configuration, namely acute or obtuse trapezoid central configuration. We also prove the existence of non–symmetric trapezoid central configurations with two pairs of equal masses.
Peer Reviewed We classify all planar four–body central configurations where two pairs of the bodies are on parallel lines. Using cartesian coordinates, we show that the set of four–body trapezoid central configurations with positive masses forms a two–dimensional surface where two symmetric families, the rhombus and isosceles trapezoid, are on its boundary. We also prove that, for a given position of the bodies, in some cases a specific order of the masses determines the geometry of the configuration, namely acute or obtuse trapezoid central configuration. We also prove the existence of non–symmetric trapezoid central configurations with two pairs of equal masses. |
| Author | Cors, Josep M. Pérez-Chavela, Ernesto Llibre, Jaume Corbera, Montserrat |
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| Cites_doi | 10.1090/S0002-9947-1932-1501666-7 10.1134/S1560354707010042 10.5565/PUBLMAT_03176_08 10.1007/978-0-387-09724-4 10.1007/BF01228714 10.4007/annals.2012.176.1.10 10.2307/2007159 10.1137/100789701 10.1007/s00205-002-0241-6 10.1007/BF01230655 10.1007/s002220050200 10.1007/s10569-016-9672-5 10.1016/j.jmaa.2018.04.009 10.1016/j.jde.2003.10.001 10.1007/BF01418778 10.1007/s00205-006-0047-z 10.1088/0951-7715/25/2/343 10.1098/rspa.2007.0320 10.1007/s00222-005-0461-0 10.1090/S0002-9904-1973-13254-9 10.1017/S0308210511000576 10.1016/j.amc.2012.12.036 10.1002/asna.19001520302 10.1007/s002050100183 10.1007/BF02571259 10.1007/BF01389805 10.1137/130911342 10.1007/s00205-017-1134-z 10.1007/BF01230241 10.1090/conm/198/02494 10.1016/j.amc.2014.07.109 |
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| References | Long, Sun (bib0024) 2002; 162 Smale (bib0038) 1970; 11 Dziobek (bib0015) 1900; 152 Barros, Leandro (bib0010) 2011; 43 Cors, Roberts (bib0014) 2012; 25 Pedersen (bib0030) 1944; 21 Albouy, Fu (bib0004) 2007; 12 Hampton, Moeckel (bib0020) 2006; 163 Gannaway (bib0018) 1981 MacMillan, Bartky (bib0025) 1932; 34 Bálin, Zalán (bib0009) 2016; 125 Bernat, Llibre, Perez-Chavela (bib0012) 2009; 16 Hagihara (bib0019) 1970 Leandro (bib0022) 2003; 167 Simó (bib0036) 1978; 18 Barros, Leandro (bib0011) 2014; 46 Álvarez, Llibre (bib0007) 2013; 219 Lagrange (bib0021) 1873 Smale (bib0037) 1970; 10 Arenstorf (bib0008) 1982; 28 Santoprete (bib0034) 2018; 464 Xia (bib0040) 2004; 200 Fernandes, Llibre, Mello (bib0017) 2017; 226 Wintner (bib0039) 1941; 5 Pérez-Chavela, Santoprete (bib0031) 2007; 185 Schmidt (bib0035) 2002 Albouy, Chenciner (bib0003) 1998; 131 Moulton (bib0028) 1910; 12 Meyer, Hall, Offin (bib0026) 2009 Albouy, Fu, Sun (bib0006) 2008; 464 Albouy, Kaloshin (bib0005) 2012; 176 Corbera, Llibre (bib0013) 2014; 246 Palmore (bib0029) 1973; 79 Moeckel (bib0027) 1990; 205 Euler (bib0016) 1767; 11 Saari (bib0032) 1980; 21 Albouy (bib0001) 1995; 320 Xie (bib0041) 2012; 142 Albouy (bib0002) 1996; 198 Llibre (bib0023) 1976; 3 Saari (bib0033) 2005; 104 Albouy (10.1016/j.amc.2018.10.066_bib0005) 2012; 176 Smale (10.1016/j.amc.2018.10.066_bib0038) 1970; 11 Fernandes (10.1016/j.amc.2018.10.066_bib0017) 2017; 226 Wintner (10.1016/j.amc.2018.10.066_bib0039) 1941; 5 Moulton (10.1016/j.amc.2018.10.066_bib0028) 1910; 12 Moeckel (10.1016/j.amc.2018.10.066_bib0027) 1990; 205 Simó (10.1016/j.amc.2018.10.066_bib0036) 1978; 18 Llibre (10.1016/j.amc.2018.10.066_bib0023) 1976; 3 Schmidt (10.1016/j.amc.2018.10.066_bib0035) 2002 Albouy (10.1016/j.amc.2018.10.066_bib0001) 1995; 320 Palmore (10.1016/j.amc.2018.10.066_bib0029) 1973; 79 Euler (10.1016/j.amc.2018.10.066_bib0016) 1767; 11 Álvarez (10.1016/j.amc.2018.10.066_bib0007) 2013; 219 Santoprete (10.1016/j.amc.2018.10.066_bib0034) 2018; 464 Gannaway (10.1016/j.amc.2018.10.066_bib0018) 1981 Cors (10.1016/j.amc.2018.10.066_bib0014) 2012; 25 Leandro (10.1016/j.amc.2018.10.066_bib0022) 2003; 167 Albouy (10.1016/j.amc.2018.10.066_bib0004) 2007; 12 Dziobek (10.1016/j.amc.2018.10.066_bib0015) 1900; 152 Pérez-Chavela (10.1016/j.amc.2018.10.066_bib0031) 2007; 185 Saari (10.1016/j.amc.2018.10.066_bib0032) 1980; 21 Albouy (10.1016/j.amc.2018.10.066_bib0002) 1996; 198 Hagihara (10.1016/j.amc.2018.10.066_bib0019) 1970 Barros (10.1016/j.amc.2018.10.066_bib0010) 2011; 43 Corbera (10.1016/j.amc.2018.10.066_bib0013) 2014; 246 Smale (10.1016/j.amc.2018.10.066_bib0037) 1970; 10 Saari (10.1016/j.amc.2018.10.066_sbref0032) 2005; 104 Xie (10.1016/j.amc.2018.10.066_bib0041) 2012; 142 Barros (10.1016/j.amc.2018.10.066_bib0011) 2014; 46 Albouy (10.1016/j.amc.2018.10.066_bib0003) 1998; 131 Long (10.1016/j.amc.2018.10.066_bib0024) 2002; 162 Xia (10.1016/j.amc.2018.10.066_bib0040) 2004; 200 Arenstorf (10.1016/j.amc.2018.10.066_bib0008) 1982; 28 Bálin (10.1016/j.amc.2018.10.066_bib0009) 2016; 125 Albouy (10.1016/j.amc.2018.10.066_bib0006) 2008; 464 MacMillan (10.1016/j.amc.2018.10.066_bib0025) 1932; 34 Lagrange (10.1016/j.amc.2018.10.066_bib0021) 1873 Hampton (10.1016/j.amc.2018.10.066_bib0020) 2006; 163 Bernat (10.1016/j.amc.2018.10.066_bib0012) 2009; 16 Pedersen (10.1016/j.amc.2018.10.066_bib0030) 1944; 21 Meyer (10.1016/j.amc.2018.10.066_bib0026) 2009 |
| References_xml | – volume: 12 start-page: 39 year: 2007 end-page: 55 ident: bib0004 article-title: Euler configurations and quasi polynomial systems publication-title: Regul. Chaotic Dyn. – volume: 142 start-page: 665 year: 2012 end-page: 672 ident: bib0041 article-title: Isosceles trapezoid central configurations of the newtonian four-body problem publication-title: Proc. R. Soc. Edinb. Sect. A Math. – volume: 464 start-page: 1355 year: 2008 end-page: 1365 ident: bib0006 article-title: Symmetry of planar four-body convex central configurations publication-title: Proc. R. Soc. Lond. Ser. A – volume: 16 start-page: 1 year: 2009 end-page: 13 ident: bib0012 article-title: On the planar central configurations of the 4–body problem with three equal masses publication-title: Dyn. Contin. Discret. Impuls. Syst. Ser. A Math. Anal. – year: 1970 ident: bib0019 publication-title: Celestial Mechanics, Vol. 1 – volume: 34 start-page: 838 year: 1932 end-page: 875 ident: bib0025 article-title: Permanent configurations in the problem of four bodies publication-title: Trans. Am. Math. Soc. – volume: 46 start-page: 1185 year: 2014 end-page: 1203 ident: bib0011 article-title: Bifurcations and enumeration of classes of relative equilibria in the planar restricted four–body problem publication-title: SIAM J. Math. Anal. – volume: 219 start-page: 5996 year: 2013 end-page: 6001 ident: bib0007 article-title: The symmetric central configurations of a 4–body problem with masses publication-title: Appl. Math. Comput. – volume: 176 start-page: 535 year: 2012 end-page: 588 ident: bib0005 article-title: Finiteness of central configurations of five bodies in the plane publication-title: Ann. Math. – volume: 18 start-page: 165 year: 1978 end-page: 184 ident: bib0036 article-title: Relative equilibrium solutions in the four-body problem publication-title: Cell Mech. – volume: 320 start-page: 217 year: 1995 end-page: 220 ident: bib0001 article-title: Symétrie des configurations centrales de quatre corps publication-title: C. R. Acad. Sci. Paris – volume: 185 start-page: 481 year: 2007 end-page: 494 ident: bib0031 article-title: Convex four-body central configurations with some equal masses publication-title: Arch. Ration. Mech. Anal. – volume: 11 start-page: 144 year: 1767 end-page: 151 ident: bib0016 article-title: De moto rectilineo trium corporum se mutuo attahentium publication-title: Novi Comm. Acad. Sci. Imp. Petrop. – volume: 104 year: 2005 ident: bib0033 article-title: Collisions, rings, and other newtonian publication-title: Am. Math. Soc. – volume: 25 start-page: 343 year: 2012 end-page: 370 ident: bib0014 article-title: Four-body co-circular central configurations publication-title: Nonlinearity – volume: 3 start-page: 73 year: 1976 end-page: 88 ident: bib0023 article-title: Posiciones de equilibrio realtivo del problema de 4 cuerpos publication-title: Publ. Mat. UAB – volume: 11 start-page: 45 year: 1970 end-page: 64 ident: bib0038 article-title: Topology and mechanics II. the planar n-body problem publication-title: Invent. Math. – volume: 167 start-page: 147 year: 2003 end-page: 177 ident: bib0022 article-title: Finiteness and bifurcation of some symmetrical classes of central configurations publication-title: Arch. Ration. Mech. Anal. – volume: 200 start-page: 185 year: 2004 end-page: 190 ident: bib0040 article-title: Convex central configurations for the publication-title: J. Differ. Equ. – volume: 152 start-page: 32 year: 1900 end-page: 46 ident: bib0015 article-title: Über einen merkwürdigen fall des vielkörperproblems publication-title: Astro. Nach. – volume: 163 start-page: 289 year: 2006 end-page: 312 ident: bib0020 article-title: Finiteness of relative equilibria of the four-body problem publication-title: Invent. Math. – year: 1981 ident: bib0018 publication-title: Determination of all Central Configurations in the Planar 4–Body Problem with One Inferior Mass – volume: 79 start-page: 904 year: 1973 end-page: 907 ident: bib0029 article-title: Classifying relative equilibria publication-title: Bull. Am. Math. Soc. – volume: 28 start-page: 9 year: 1982 end-page: 15 ident: bib0008 article-title: Central configurations of four bodies with one inferior mass publication-title: Cell Mech. – volume: 131 start-page: 151 year: 1998 end-page: 184 ident: bib0003 article-title: Le problème des publication-title: Invent. Math. – volume: 125 start-page: 33 year: 2016 end-page: 70 ident: bib0009 article-title: Central configurations of four bodies with an axis of symmetry publication-title: Celest. Mech. Dyn. Astron. – volume: 226 start-page: 303 year: 2017 end-page: 320 ident: bib0017 article-title: Convex central configurations of the 4–body problem with two pairs of equal adjacent masses publication-title: Arch. Ration. Mech. Anal. – volume: 21 start-page: 9 year: 1980 end-page: 20 ident: bib0032 article-title: On the role and properties of central configurations publication-title: Celestial Mech. – volume: 246 start-page: 121 year: 2014 end-page: 147 ident: bib0013 article-title: Central configurations of the 4–body problem with masses publication-title: Appl. Math. Comput. – year: 2009 ident: bib0026 article-title: Introduction to hamiltonian dynamical systems and the publication-title: Applied Mathematica l Sciences, 90 – volume: 464 start-page: 421 year: 2018 end-page: 434 ident: bib0034 article-title: Four-body central configurations with one pair of opposite sides parallel publication-title: J. Math. Anal. Appl. – volume: 10 start-page: 305 year: 1970 end-page: 331 ident: bib0037 article-title: Topology and mechanics i publication-title: Invent. Math. – volume: 198 start-page: 131 year: 1996 end-page: 135 ident: bib0002 article-title: The symmetric central configurations of four equal masses publication-title: Contemp. Math. – year: 1873 ident: bib0021 article-title: Essai sur le problème de toris corps publication-title: Ouvres, Vol. 6 – volume: 12 start-page: 1 year: 1910 end-page: 17 ident: bib0028 article-title: The straight line solutions of publication-title: Ann. Math. – volume: 205 start-page: 499 year: 1990 end-page: 517 ident: bib0027 article-title: On central configurations publication-title: Math. Z. – volume: 43 start-page: 634 year: 2011 end-page: 661 ident: bib0010 article-title: The set of degenerate cetral configurations in the planar restricted four–body problem publication-title: SIAM J. Math. Anal. – volume: 21 start-page: 1 year: 1944 end-page: 80 ident: bib0030 article-title: Librationspunkte im restringierten vierk orperproblem publication-title: Danske Vid. Selsk. Math.–Fys. – volume: 162 start-page: 24 year: 2002 end-page: 44 ident: bib0024 article-title: Four–body central configurations with some equal masses publication-title: Arch. Ration. Mech. Anal. – start-page: 1 year: 2002 end-page: 33 ident: bib0035 article-title: Central configurations and relative equilibria for the publication-title: Classical and Celestial Mechanics (Recife, 1993/1999) – volume: 5 year: 1941 ident: bib0039 article-title: The analytical foundations of celestial mechanics publication-title: Princeton Mathematical Series – volume: 34 start-page: 838 year: 1932 ident: 10.1016/j.amc.2018.10.066_bib0025 article-title: Permanent configurations in the problem of four bodies publication-title: Trans. Am. Math. Soc. doi: 10.1090/S0002-9947-1932-1501666-7 – volume: 12 start-page: 39 year: 2007 ident: 10.1016/j.amc.2018.10.066_bib0004 article-title: Euler configurations and quasi polynomial systems publication-title: Regul. Chaotic Dyn. doi: 10.1134/S1560354707010042 – volume: 3 start-page: 73 year: 1976 ident: 10.1016/j.amc.2018.10.066_bib0023 article-title: Posiciones de equilibrio realtivo del problema de 4 cuerpos publication-title: Publ. Mat. UAB doi: 10.5565/PUBLMAT_03176_08 – year: 2009 ident: 10.1016/j.amc.2018.10.066_bib0026 article-title: Introduction to hamiltonian dynamical systems and the n-body problem doi: 10.1007/978-0-387-09724-4 – volume: 18 start-page: 165 year: 1978 ident: 10.1016/j.amc.2018.10.066_bib0036 article-title: Relative equilibrium solutions in the four-body problem publication-title: Cell Mech. doi: 10.1007/BF01228714 – volume: 176 start-page: 535 issue: 2 year: 2012 ident: 10.1016/j.amc.2018.10.066_bib0005 article-title: Finiteness of central configurations of five bodies in the plane publication-title: Ann. Math. doi: 10.4007/annals.2012.176.1.10 – volume: 12 start-page: 1 year: 1910 ident: 10.1016/j.amc.2018.10.066_bib0028 article-title: The straight line solutions of n bodies publication-title: Ann. Math. doi: 10.2307/2007159 – volume: 43 start-page: 634 year: 2011 ident: 10.1016/j.amc.2018.10.066_bib0010 article-title: The set of degenerate cetral configurations in the planar restricted four–body problem publication-title: SIAM J. Math. Anal. doi: 10.1137/100789701 – year: 1873 ident: 10.1016/j.amc.2018.10.066_bib0021 article-title: Essai sur le problème de toris corps – volume: 167 start-page: 147 year: 2003 ident: 10.1016/j.amc.2018.10.066_bib0022 article-title: Finiteness and bifurcation of some symmetrical classes of central configurations publication-title: Arch. Ration. Mech. Anal. doi: 10.1007/s00205-002-0241-6 – volume: 28 start-page: 9 year: 1982 ident: 10.1016/j.amc.2018.10.066_bib0008 article-title: Central configurations of four bodies with one inferior mass publication-title: Cell Mech. doi: 10.1007/BF01230655 – volume: 104 year: 2005 ident: 10.1016/j.amc.2018.10.066_sbref0032 article-title: Collisions, rings, and other newtonian n-body problems, in: CBMS regional conference series in mathematics, no. publication-title: Am. Math. Soc. – volume: 5 year: 1941 ident: 10.1016/j.amc.2018.10.066_bib0039 article-title: The analytical foundations of celestial mechanics – volume: 131 start-page: 151 year: 1998 ident: 10.1016/j.amc.2018.10.066_bib0003 article-title: Le problème des n corps et les distances mutuelles publication-title: Invent. Math. doi: 10.1007/s002220050200 – volume: 125 start-page: 33 year: 2016 ident: 10.1016/j.amc.2018.10.066_bib0009 article-title: Central configurations of four bodies with an axis of symmetry publication-title: Celest. Mech. Dyn. Astron. doi: 10.1007/s10569-016-9672-5 – volume: 464 start-page: 421 year: 2018 ident: 10.1016/j.amc.2018.10.066_bib0034 article-title: Four-body central configurations with one pair of opposite sides parallel publication-title: J. Math. Anal. Appl. doi: 10.1016/j.jmaa.2018.04.009 – volume: 200 start-page: 185 year: 2004 ident: 10.1016/j.amc.2018.10.066_bib0040 article-title: Convex central configurations for the n-body problem publication-title: J. Differ. Equ. doi: 10.1016/j.jde.2003.10.001 – volume: 10 start-page: 305 year: 1970 ident: 10.1016/j.amc.2018.10.066_bib0037 article-title: Topology and mechanics i publication-title: Invent. Math. doi: 10.1007/BF01418778 – volume: 185 start-page: 481 year: 2007 ident: 10.1016/j.amc.2018.10.066_bib0031 article-title: Convex four-body central configurations with some equal masses publication-title: Arch. Ration. Mech. Anal. doi: 10.1007/s00205-006-0047-z – volume: 25 start-page: 343 year: 2012 ident: 10.1016/j.amc.2018.10.066_bib0014 article-title: Four-body co-circular central configurations publication-title: Nonlinearity doi: 10.1088/0951-7715/25/2/343 – volume: 464 start-page: 1355 year: 2008 ident: 10.1016/j.amc.2018.10.066_bib0006 article-title: Symmetry of planar four-body convex central configurations publication-title: Proc. R. Soc. Lond. Ser. A doi: 10.1098/rspa.2007.0320 – volume: 163 start-page: 289 year: 2006 ident: 10.1016/j.amc.2018.10.066_bib0020 article-title: Finiteness of relative equilibria of the four-body problem publication-title: Invent. Math. doi: 10.1007/s00222-005-0461-0 – volume: 79 start-page: 904 year: 1973 ident: 10.1016/j.amc.2018.10.066_bib0029 article-title: Classifying relative equilibria publication-title: Bull. Am. Math. Soc. doi: 10.1090/S0002-9904-1973-13254-9 – volume: 21 start-page: 1 year: 1944 ident: 10.1016/j.amc.2018.10.066_bib0030 article-title: Librationspunkte im restringierten vierk orperproblem publication-title: Danske Vid. Selsk. Math.–Fys. – volume: 142 start-page: 665 year: 2012 ident: 10.1016/j.amc.2018.10.066_bib0041 article-title: Isosceles trapezoid central configurations of the newtonian four-body problem publication-title: Proc. R. Soc. Edinb. Sect. A Math. doi: 10.1017/S0308210511000576 – volume: 219 start-page: 5996 year: 2013 ident: 10.1016/j.amc.2018.10.066_bib0007 article-title: The symmetric central configurations of a 4–body problem with masses m1=m2≠m3=m4 publication-title: Appl. Math. Comput. doi: 10.1016/j.amc.2012.12.036 – volume: 16 start-page: 1 year: 2009 ident: 10.1016/j.amc.2018.10.066_bib0012 article-title: On the planar central configurations of the 4–body problem with three equal masses publication-title: Dyn. Contin. Discret. Impuls. Syst. Ser. A Math. Anal. – year: 1981 ident: 10.1016/j.amc.2018.10.066_bib0018 – start-page: 1 year: 2002 ident: 10.1016/j.amc.2018.10.066_bib0035 article-title: Central configurations and relative equilibria for the n-body problem – volume: 152 start-page: 32 year: 1900 ident: 10.1016/j.amc.2018.10.066_bib0015 article-title: Über einen merkwürdigen fall des vielkörperproblems publication-title: Astro. Nach. doi: 10.1002/asna.19001520302 – volume: 162 start-page: 24 year: 2002 ident: 10.1016/j.amc.2018.10.066_bib0024 article-title: Four–body central configurations with some equal masses publication-title: Arch. Ration. Mech. Anal. doi: 10.1007/s002050100183 – volume: 205 start-page: 499 year: 1990 ident: 10.1016/j.amc.2018.10.066_bib0027 article-title: On central configurations publication-title: Math. Z. doi: 10.1007/BF02571259 – volume: 11 start-page: 45 year: 1970 ident: 10.1016/j.amc.2018.10.066_bib0038 article-title: Topology and mechanics II. the planar n-body problem publication-title: Invent. Math. doi: 10.1007/BF01389805 – year: 1970 ident: 10.1016/j.amc.2018.10.066_bib0019 – volume: 46 start-page: 1185 year: 2014 ident: 10.1016/j.amc.2018.10.066_bib0011 article-title: Bifurcations and enumeration of classes of relative equilibria in the planar restricted four–body problem publication-title: SIAM J. Math. Anal. doi: 10.1137/130911342 – volume: 226 start-page: 303 year: 2017 ident: 10.1016/j.amc.2018.10.066_bib0017 article-title: Convex central configurations of the 4–body problem with two pairs of equal adjacent masses publication-title: Arch. Ration. Mech. Anal. doi: 10.1007/s00205-017-1134-z – volume: 21 start-page: 9 year: 1980 ident: 10.1016/j.amc.2018.10.066_bib0032 article-title: On the role and properties of central configurations publication-title: Celestial Mech. doi: 10.1007/BF01230241 – volume: 320 start-page: 217 year: 1995 ident: 10.1016/j.amc.2018.10.066_bib0001 article-title: Symétrie des configurations centrales de quatre corps publication-title: C. R. Acad. Sci. Paris – volume: 198 start-page: 131 year: 1996 ident: 10.1016/j.amc.2018.10.066_bib0002 article-title: The symmetric central configurations of four equal masses publication-title: Contemp. Math. doi: 10.1090/conm/198/02494 – volume: 246 start-page: 121 year: 2014 ident: 10.1016/j.amc.2018.10.066_bib0013 article-title: Central configurations of the 4–body problem with masses m1=m2>m3=m4=m>0 and m small publication-title: Appl. Math. Comput. doi: 10.1016/j.amc.2014.07.109 – volume: 11 start-page: 144 year: 1767 ident: 10.1016/j.amc.2018.10.066_bib0016 article-title: De moto rectilineo trium corporum se mutuo attahentium publication-title: Novi Comm. Acad. Sci. Imp. Petrop. |
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| Snippet | We classify all planar four–body central configurations where two pairs of the bodies are on parallel lines. Using cartesian coordinates, we show that the set... |
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| SubjectTerms | 37 Dynamical systems and ergodic theory 37N Applications 4-body problem 70 Mechanics of particles and systems 70F Dynamics of a system of particles, including celestial mechanics Classificació AMS Configurations Convex central configurations Enginyeria mecànica Many-body problem Matemàtiques i estadística Problema dels cossos múltiples Trapezoidal central configurartions Àrees temàtiques de la UPC |
| Title | Trapezoid central configurations |
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