Central configurations of the circular restricted 4-body problem with three equal primaries in the collinear central configuration of the-3 body problem
Article Sidebar
Main Article Content
Abstract
In this paper we classify the central configurations of the circular restricted 4-body problem with three primaries with equal masses at the collinear configuration of the 3-body problem and an infinitisimal mass.
Downloads
Article Details
Copyright (c) 2021 Llibre J.
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.
Wintner A (1941) The Analytical Foundations of Celestial Mechanics, Princeton University Press. Link: https://bit.ly/3n7ci8v
Meyer KR (1987) Bifurcation of a central configuration. Celestial Mech 40: 273-282. Link: https://bit.ly/3o7RcIl
Smale S (1970) Topology and mechanics II: The planar n–body problem. Inventiones math 11: 45-64. Link: https://bit.ly/3rNgltW
Gómez G (2001) Dynamics and Mission Design Near Libration Points. Vol. I Fundamentals: The case of collinear libration points, World Scientific Monograph Series in Mathematics 2. Link: https://bit.ly/387zjUc
Gómez G (2001) Dynamics and Mission Design Near Libration Points. Vol. I Fundamentals: The case of collinear libration points, World Scientific Monograph Series in Mathematics 2. Link: https://bit.ly/387zjUc
Euler L (1767) De moto rectilineo trium corporum se mutuo attahentium. Novi Comm Acad Sci Imp Petrop 11: 144-151. Link: https://bit.ly/38S8Jhg
Lagrange JL (1873) Essai surle probleme des trois corps, recueil des pieces qui ont remporte le prix de l’Academie royale des Sciences de Paris,tome IX, 1772, reprinted in Ouvres 6: 229–324.
Hagihara Y (1970) Celestial Mechanics. 1. MIT Press, Massachusetts.
Llibre J (1991) On the number of central configurations in the n-body problem. Celestial Mech Dynam Astronom 50: 89-96. Link:
Llibre J (2017) On the central configurations of the n-body problem. Appl Math Nonlinear Sci 2: 509-518. Link: https://bit.ly/2JHHBZS
Moeckel R (1990) On central configurations. Math Zeitschrift 205: 499-517. Link: https://bit.ly/3hM34xr
Saari DG (1980) On the role and properties of central configurations. Celestial Mech 21: 9-20. Link: https://bit.ly/3862ZRV
Albouy A (1995) Symetrie des configurations centrales de quatre corps. CR Acad Sci Paris 320: 217-220. Link: https://www.semanticscholar.org/paper/Sym%C3%A9trie-des-configurations-centrales-de-quatre-Albouy/4408d2a8d129b375cc5eae706f6ddc5583a238e1
Albouy A (1995) The symmetric central configurations of four equal masses, Hamiltonian dynamics and celestial mechanics (Seattle, WA, 1995). 131–135, Contemp. Math. 198, Amer. Math. Soc., Providence, RI, 1996. Link:
Albouy A, Fu Y, Sun S (2008) Symmetry of planar four body convex central configurations. Proc R Soc Lond Ser A Math Phys Eng Sci 464: 1355-1365. Link: https://hal.archives-ouvertes.fr/hal-00153212
Albouy A, Kaloshin V (2012) Finiteness of central configurations of five bodies in the plane. Ann Math 176: 535-588. Link: https://annals.math.princeton.edu/2012/176-1/p10
lvarez-RamÃrez M, Corbera M, Delgado J, Llibre J (2004) The number of planar central configurations for the 4-body problem is finite when 3 mass positions are fixed. Proc Amer Math Soc 133: 529-536. Link: https://bit.ly/3pLCMOx
lvarez-RamÃrez M, Delgado J (2003) Central configurations of the symmetric restricted 4-body problem. Celestial Mech Dynam Astronom 87: 371-381. Link: https://bit.ly/3b0YhGM
lvarez-RamÃrez M, Llibre J (2013) The symmetric central configurations of the 4-body problem with masses. Appl Math Comp 219: 5996-6001. Link: https://bit.ly/3pBge2E
lvarez-RamÃrez M, Llibre J (2018) Hjelmslev quadrilateral central configurations. Physics Letters A 383: 103-109. Link: https://bit.ly/3pA85eW
lvarez-RamÃrez M, Llibre J (2019) Equilic quadrilateral central configurations. Commun Nonlinear Sci Numer Simul 78: 104872. Link: https://bit.ly/3hyuiHw
Alvarez-Ramirez A, Santos AA, Vidal C (2013) On co-circular central configurations in the four and five body-problem for homogeneous force law. J Dynam Differential Equations 25: 269-290. Link: https://bit.ly/3ob5Tui
Arribas M, Abad A, Elipe A, Palacios M (2016) Equilibria of the symmetric collinear restricted four-body problem with radiation pressure, Astrophys. Space Sci 361: 12. Link: https://bit.ly/38UNfAe
Arenstorf RF (1982) Central configurations of four bodies with one inferior mass. Cel Mechanics 28: 9-15. Link: https://bit.ly/3aWsRBv
Barros JF, Leandro ESG (2011) The set of degenerate central configurations in the planar restricted four-body problem. SIAM Journal on Mathematical Analysis 43: 634-661. Link: https://bit.ly/3hyufvk
Barros JF, Leandro ESG (2014) Bifurcations and enumeration of classes of relative equilibria in the planar restricted four-body problem. SIAM Joural on Mathematical Analysis 46: 1185-1203. Link: https://bit.ly/3pK1aQi
Bernat J, Llibre J, Perez-Chavela E (2009) On the planar central configurations of the 4-body problem with three equal masses. Dyn Contin Discrete Impuls. Syst Ser A Math Anal 16: 1-13.
Chenciner A (2017) Are nonsymmetric balanced configurations of four equal masses virtual or real?. Regul Chaotic Dyn 22: 677-687. Link: https://bit.ly/3rIlWBQ
Corbera M, Cors JM, Llibre J, Perez-Chavela E (2019) Trapezoid central configurations. Appl Math Comput 346: 127-142. Link: https://bit.ly/3n5WCSW
Corbera M, Llibre J (2014) Central configurations of the 4-body problem with masses m1=m2>m3=m4=m>0 and m small. Appl Math Comput 246: 121-147. Link: https://bit.ly/2MpY0Dc
Corbera M, Cors JM, Llibre J (2011) On the central configurations of the planar -body problem. Celestial Mech Dynam Astronom 109: 27-43.
Corbera M, Cors JM, Roberts GE (2018) A four-body convex central configurationGwith perpendicular diagonals is necessarily a kite. Qual Theory Dyn Syst 17: 367-374. Link: https://bit.ly/3bdf8GL
Corbera M, Cors JM, Roberts GE (2019) Classifying four-body convex central configurations. Celestial Mech Dynam Astronom 131: 34. Link: https://bit.ly/3hykFst
Cors JM, Roberts GE (2012) Four-body co-circular central configurations. Nonlinearity 25: 343-370. Link: https://bit.ly/2MrdKG0
Cors JM, Llibre J, Ollé M (2004) Central configurations of the planar coorbital satellite problem. Celestial Mech Dynam Astronom 89: 319-342. Link: https://bit.ly/2LhG1hO
Deng Y, Li B, Zhang S (2017) Four-body central configurations with adjacent equal masses. J Geom Phys 114: 329-335. Link: https://bit.ly/38LAI1S
Deng Y, Li B, Zhang S (2017) Some notes on four-body co-circular central configurations. J Math Anal Appl 453: 398-409. Link: https://bit.ly/3hxqo1I
Deng C, Zhang S (2014) Planar symmetric concave central configurations in Newtonian four-body problems. J Geom Phys 83: 43-52. Link: https://bit.ly/3pMVwgF
Rdi B, Czirj KZ (2016) Central configuration of four bodies with an axis of symmetry. Celestial Mech Dynam Astronom 125: 33-70. Link: https://bit.ly/2MqBEkZ
Fernandes AC, Llibre J, Mello LF (2017) Convex central configurations of the 4-body problem with two pairs of equal masses. Arch Rational Mech Anal 226: 303-320. Link: https://bit.ly/38O6FXw
Gannaway JR (1981) Determination of all central configurations in the planar 4-body problem with one inferior mass, Ph. D., Vanderbilt University, Nashville, USA.
Fernandes AC, Garcia BA, Llibre J, Mello LF (2018) New central configurations of the (n+1) body problem. J Geom Phys 124: 199-207. Link: https://bit.ly/3rL2K6m
Grebenikov EA, Ikhsanov EV, Prokopenya AN (2006) Numeric-symbolic computations in the study of central configurations in the planar Newtonian four-body problem, Computer algebra in scientific computing, 192–204. Lecture Notes Comput Sci. Link:
Hampton M (2003) Co-circular central configurations in the four-body problem. EQUADIFF 993–998. Link: https://bit.ly/38Wj63F
Hampton M, Moeckel R (2006) Finiteness of relative equilibria of the four-body problem. Invent Math 163: 289-312. Link: https://bit.ly/34YmsSj
Hassan MR, Ullah MS, Aminul HM, Prasad U (2017) Applications of planar Newtonian four-body problem to the central configurations. Appl Appl Math 12: 1088-1108. Link: https://bit.ly/3hycLiP
Leandro ESG (2006) On the central configurations of the planar restricted four-body problem. J Differential Equations 226: 323-351. Link: https://bit.ly/3o8Wovk
Llibre J (1976) Posiciones de equilibrio relativo del problema de 4 cuerpos. Publicacions Matemàtiques UAB 3: 73-88. Link: https://bit.ly/2KMCZCi
Llibre J, Yuan P (2019) Bicentric quadrilateral central configurations. Appl Math Comput 362: 124507. Link: https://bit.ly/3rLKyK0
Llibre J, Yuan P (2020) Tangential trapezoid central configurations. Regul Chaotic Dyn 25: 651-661. Link: https://bit.ly/2X3F6nG
Long Y (2003) Admissible shapes of 4-body non-collinear relative equilibria. Adv Nonlinear Stud 3: 495-509. Link: https://bit.ly/387q5rc
Long Y, Sun S (2002) Four-Body Central Configurations with some Equal Masses. Arch Ration Mech Anal 162: 25-44. Link: https://bit.ly/3b89Zzk
MacMillan WD, Bartky W (1932) Permanent Configurations in the Problem of Four Bodies. Trans Amer Math Soc 34: 838-875. Link: https://bit.ly/2X3EYVe
Ouyang T, Xie Z (2005) Collinear central configuration in four-body problem. Celestial Mech Dynam Astronom 93: 147-166. Link: https://bit.ly/3hzJPqA
Pedersen P (1944) Librationspunkte im restringierten Vierkörperproblem. Danske Vid Selsk Math Fys 21: 1-80. Link: https://bit.ly/3b1ftMA
Perez-Chavela E, Santoprete M (2007) Convex four-body central configurations with some equal masses. Arch Rational Mech Anal 185: 481-494. Link: https://bit.ly/3naQzMB
Pina E (2013) Computing collinear 4-body problem central configurations with given masse. Discrete Contin. Dyn Syst 33: 1215–1230. Link: https://bit.ly/38UbE9e
Pina E, Lonngi P (2010) Central configuration for the planar Newtonian four-body problem. Celest Mech Dyn Astron 108: 73-93. Link: https://bit.ly/2LdRAWW
Rusu D, Santoprete M (2016) Bifurcations of central configurations in the four-body problem with some equal masses. SIAM J Appl Dyn Syst 15: 440-458. Link: https://bit.ly/2KWIGgK
Shi J, Xie Z (2010) Classification of four-body central configurations with three equal masses. J Math Anal Appl 363: 512-524. Link: https://bit.ly/2LdKiTn
Shoaib M, Kashif AR, Szücs-Csillik I (2017) On the planar central configurations of rhomboidal and triangular four- and five-body problems. Astrophys Space Sci 362: 182. Link: https://bit.ly/2L7l4G5
Simo C (1978) Relative equilibrium solutions in the four-body problem. Cel Mechanics 18: 165-184. Link: https://bit.ly/3pFMbXJ
Tang JL (2006) A study on the central configuration in the Newtonian 4-body problem of celestial mechanics (Chinese). J Systems Sci Math Sci 26: 647-650.
Xie Z (2012) Isosceles trapezoid central configurations of the Newtonian four-body problem. Proc Roy Soc Edinburgh Sect A 142: 665-672. Link: https://bit.ly/3o6LlD5
Yoshimi N, Yoshioka A (2018) 3+1 Moulton configuration. SUT J Math 54: 173-190.
Herget P (1967) Theory of orbits, The restricted problem of three bodies, Academic Press, New York. Link: https://bit.ly/3n7ki9a
Bernat J, Llibre J, Perez-Chavela E (2009) On the planar central configurations of the 4-body problem with three equal masses. Dyn Contin Discrete Impuls. Syst Ser A Math Anal 16: 1-13.
Stoer J, Bulirsch R (1980) Introduction to numerical analysis, Springer-Verlag, New York. Link: https://bit.ly/3521NNi