Electron. J. Diff. Eqns., Vol. 2004(2004), No. 106, pp. 1-9.

Pyramidal central configurations and perverse solutions

Tiancheng Ouyang, Zhifu Xie, Shiqing Zhang

Abstract:
For $n$-body problems, a central configuration (CC) plays an important role. In this paper, we establish the relation between the spatial pyramidal central configuration (PCC) and the planar central configuration. We prove that the base of PCC is also a CC and we also prove that for some given conditions a planar CC can be extended to a PCC. In particular, if the pyramidal central configuration has a regular polygon base, then the masses of base are equal and the distance between the top vertex and the base is fixed and the mass of the top vertex is selective. Furthermore, the pyramidal central configuration gives rise to an example of a perverse solution in $\mathbb{R}^3$.

Submitted December 6, 2003. Published September 10, 2004.
Math Subject Classifications: 37N05, 70F10, 70F15.
Key Words: n-body problems; pyramidal central configuration; regular polygonal base; perverse solutions.

Show me the PDF file (205K), TEX file, and other files for this article.

  Tiancheng Ouyang
Department of Mathematics, Brigham Young University
Provo, Utah 84604, USA
email: ouyang@math.byu.edu
Zhifu Xie
Department of Mathematics, Brigham Young University
Provo, Utah 84604, USA
email: zhifu@math.byu.edu
  Shiqing Zhang
Department of Mathematics
Yangzhou University, Yangzhou, China
email: shiqing2001@163.net

Return to the EJDE web page