On the planar central configurations of rhomboidal and triangular four- and five-body problems

被引：10
|
作者：
Shoaib, Muhammad [1 ]
Kashif, Abdul Rehman [2 ]
Szucs-Csillik, Iharka [3 ]
机构：
[1] Abu Dhabi Mens Coll, Higher Coll Technol, POB 25035, Abu Dhabi, U Arab Emirates
[2] Capital Univ Sci & Technol, Dept Math, Islamabad, Pakistan
[3] Romanian Acad, Astron Inst, Ciresilor 19, Cluj Napoca 400487, Romania
来源：
ASTROPHYSICS AND SPACE SCIENCE | 2017年 / 362卷 / 10期
关键词：
Central configuration; n-Body problem; Chaos; Periodic orbits; 4-BODY PROBLEM; STABILITY; ORBITS;
D O I：
10.1007/s10509-017-3161-5
中图分类号：
P1 [天文学];
学科分类号：
0704 ;
摘要：
We consider a symmetric five-body problem with three unequal collinear masses on the axis of symmetry. The remaining two masses are symmetrically placed on both sides of the axis of symmetry. Regions of possible central configurations are derived for the four-and five-body problems. These regions are determined analytically and explored numerically. The equations of motion are regularized using Levi-Civita type transformations and then the phase space is investigated for chaotic and periodic orbits by means of Poincare surface of sections.
引用
收藏
页数：19
相关论文
共 50 条
  • [41] Spatial restricted rhomboidal five-body problem and horizontal stability of its periodic solutions
    Marcelo Marchesin
    Claudio Vidal
    Celestial Mechanics and Dynamical Astronomy, 2013, 115 : 261 - 279
  • [42] Central configurations for the planar Newtonian four-body problem
    Pina, E.
    Lonngi, P.
    CELESTIAL MECHANICS & DYNAMICAL ASTRONOMY, 2010, 108 (01): : 73 - 93
  • [43] On the central configurations of the planar restricted four-body problem
    Leandro, Eduardo S. G.
    JOURNAL OF DIFFERENTIAL EQUATIONS, 2006, 226 (01) : 323 - 351
  • [44] Central configurations for the planar Newtonian four-body problem
    E. Piña
    P. Lonngi
    Celestial Mechanics and Dynamical Astronomy, 2010, 108 : 73 - 93
  • [45] 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
  • [46] On Co-Circular Central Configurations in the Four and Five Body-Problems for Homogeneous Force Law
    Alvarez-Ramirez, Martha
    Santos, Alan Almeida
    Vidal, Claudio
    JOURNAL OF DYNAMICS AND DIFFERENTIAL EQUATIONS, 2013, 25 (02) : 269 - 290
  • [47] On Co-Circular Central Configurations in the Four and Five Body-Problems for Homogeneous Force Law
    Martha Alvarez-Ramírez
    Alan Almeida Santos
    Claudio Vidal
    Journal of Dynamics and Differential Equations, 2013, 25 : 269 - 290
  • [48] Continuation and bifurcations of concave central configurations in the four and five body-problems for homogeneous force laws
    Santos, Alan Almeida
    Marchesin, Marcelo
    Perez-Chavela, Ernesto
    Vidal, Claudio
    JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2017, 446 (02) : 1743 - 1768
  • [49] On Stacked Planar Central Configurations with Five Bodies when One Body is Removed
    Antonio Carlos Fernandes
    Luis Fernando Mello
    Qualitative Theory of Dynamical Systems, 2013, 12 : 293 - 303
  • [50] On Stacked Planar Central Configurations with Five Bodies when One Body is Removed
    Fernandes, Antonio Carlos
    Mello, Luis Fernando
    QUALITATIVE THEORY OF DYNAMICAL SYSTEMS, 2013, 12 (02) : 293 - 303
12345