Electronic Journal of Differential Equations,
Vol. 2004(2004), No. 106, pp. 1-9.

Title: Pyramidal central configurations and perverse solutions

Authors: Tiancheng Ouyang (Brigham Young Univ. Provo, Utah, USA)
         Zhifu Xie        (Brigham Young Univ. Provo, Utah, USA)
	 Shiqing Zhang    (Yangzhou Univ., Yangzhou, China}
 
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.