On the central configurations of the planar 1 + 3 body problem

被引：0
|
作者：
Montserrat Corbera
Josep Maria Cors
Jaume Llibre
机构：
[1] Universitat de Vic,Departament de Tecnologies Digitals i de la Informació
[2] Universitat Politècnica de Catalunya,Matemàtica Aplicada III
[3] Universitat Autònoma de Barcelona,Departament de Matemàtiques
[4] Bellaterra,undefined
来源：
Celestial Mechanics and Dynamical Astronomy | 2011年 / 109卷
关键词：
1 + 3 body problem; Central configurations; Coorbital satellites;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
We consider the Newtonian four-body problem in the plane with a dominat mass M. We study the planar central configurations of this problem when the remaining masses are infinitesimal. We obtain two different classes of central configurations depending on the mutual distances between the infinitesimal masses. Both classes exhibit symmetric and non-symmetric configurations. And when two infinitesimal masses are equal, with the help of extended precision arithmetics, we provide evidence that the number of central configurations varies from five to seven.
引用
收藏
页码：27 / 43
页数：16
相关论文
共 50 条
  • [41] Generic Finiteness for a Class of Symmetric Planar Central Configurations of the Six-Body Problem and the Six-Vortex Problem
    Thiago Dias
    Bo-Yu Pan
    Journal of Dynamics and Differential Equations, 2020, 32 : 1579 - 1602
  • [42] Generic Finiteness for a Class of Symmetric Planar Central Configurations of the Six-Body Problem and the Six-Vortex Problem
    Dias, Thiago
    Pan, Bo-Yu
    JOURNAL OF DYNAMICS AND DIFFERENTIAL EQUATIONS, 2020, 32 (04) : 1579 - 1602
  • [43] Linear stability of the elliptic relative equilibrium with (1+n)-gon central configurations in planar n-body problem
    Hu, Xijun
    Long, Yiming
    Ou, Yuwei
    NONLINEARITY, 2020, 33 (03) : 1016 - 1045
  • [44] Planar N-body central configurations with a homogeneous potential
    Marshall Hampton
    Celestial Mechanics and Dynamical Astronomy, 2019, 131
  • [45] Central configurations in planar n-body problem with equal masses for n=5, 6, 7
    Moczurad, Malgorzata
    Zgliczynski, Piotr
    CELESTIAL MECHANICS & DYNAMICAL ASTRONOMY, 2019, 131 (10):
  • [46] Numeric-symbolic computations in the study of central configurations in the planar Newtonian four-body problem
    Grebenikov, Evgenii A.
    Ikhsanov, Ersain V.
    Prokopenya, Alexander N.
    COMPUTER ALGEBRA IN SCIENTIFIC COMPUTING, PROCEEDINGS, 2006, 4194 : 192 - 204
  • [47] Planar N-body central configurations with a homogeneous potential
    Hampton, Marshall
    CELESTIAL MECHANICS & DYNAMICAL ASTRONOMY, 2019, 131 (05):
  • [48] Symmetry of planar four-body convex central configurations
    Albouy, Alain
    Fu, Yanning
    Sun, Shanzhong
    PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES, 2008, 464 (2093): : 1355 - 1365
  • [49] New classes of spatial central configurations for the n+3-body problem
    Mello, Luis Fernando
    Fernandes, Antonio Carlos
    NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS, 2011, 12 (01) : 723 - 730
  • [50] CENTRAL CONFIGURATIONS AND HYPERBOLIC-ELLIPTIC MOTION IN THE 3-BODY PROBLEM
    HULKOWER, ND
    CELESTIAL MECHANICS, 1980, 21 (01): : 37 - 41
12345