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.
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页码：27 / 43
页数：16
相关论文
共 16 条
  • [1] Albouy A.(2009)Relative equilibria of four identical satellites Proc. R. Soc. A 465 2633-2645
  • [2] Fu Y.(1994)Central configurations of the planar 1 +  Celest. Mech. Dyn. Astron. 60 273-288
  • [3] Casasayas J.(2004) body problem Celest. Mech. Dyn. Astron. 89 319-342
  • [4] Llibre J.(2009)Central configurations of the planar coorbital satellite problem Celest. Mech. Dyn. Astron. 104 369-381
  • [5] Nunes A.(1994)Central configurations of the five-body problem with equal masses J. Dyn. Diff. Equ. 6 37-51
  • [6] Cors J.M.(2004)Linear stability of relative equilibria with a dominant mass Celest. Mech. Dyn. Astron. 88 397-414
  • [7] Llibre J.(2000)Stationary configurations for co–orbital satellites with small arbitary masses Hamiltonian Systems and Celestial Mechanics (HAMSYS-98). World Sci. Monogr. Ser. Math. 6 303-330
  • [8] Ollé M.(1991)Linear stability of the Celest. Mech. Dyn. Astron. 51 83-103
  • [9] Lee T.-L.(undefined) + 1-gon relative equilibrium undefined undefined undefined-undefined
  • [10] Santoprete M.(undefined)Linear stability of a self-graviting rings undefined undefined undefined-undefined
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