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关于4-体问题中心构型的一点研究

汤建良   

  1. 深圳大学理学院数学系, 深圳 518060
  • 收稿日期:2005-03-04 修回日期:2005-06-07 出版日期:2006-12-25 发布日期:2006-12-25

汤建良. 关于4-体问题中心构型的一点研究[J]. 系统科学与数学, 2006, 26(6): 647-650.

Tang Jianliang. A Study on the central configuration in the newtonian 4-body problem of celestial mechanics[J]. Journal of Systems Science and Mathematical Sciences, 2006, 26(6): 647-650.

A Study on the central configuration in the newtonian 4-body problem of celestial mechanics

Tang Jianliang

  

  1. College of Science, Shenzhen University, Shenzhen, 518060
  • Received:2005-03-04 Revised:2005-06-07 Online:2006-12-25 Published:2006-12-25
N-体问题的中心构型是应用数学领域广泛研究的问题.关于N-体问题的中心构型已有许多研究结果.但是对于n[[gteq]]4,其中心构型解的计算是比较困难的.作者运用 Wu-Ritt 零点分解方法和子结式序列研究了一般的平面4体中心构型问题,给出了这类4体中心构型问题的解析解,从而证明了一类平面牛顿 4-体问题的中心构型个数是有限的.
The central configuration in the $N$-body problem is one of the most studied problems in the field of celestial mechanics and appled mathematics. There are many results about central configurations. In this paper, by using Wu-Ritt method and subresultant sequences, we study a class of Newtonian planar 4-body problem and give a closed form solution. From the solution, we prove that the configurations for a class of Newtonian planar 4-body problem is finite.

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