Abstract and Applied Analysis
Volume 2013 (2013), Article ID 272791, 5 pages
http://dx.doi.org/10.1155/2013/272791
Research Article

Central Configurations for Newtonian -Body Problems

Furong Zhao1,2 and Jian Chen1,3

1Department of Mathematics, Sichuan University, Chengdu, Sichuan 610064, China
2Department of Mathematics and Computer Science, Mianyang Normal University, Mianyang, Sichuan 621000, China
3Department of Mathematics, Southwest University of Science and Technology, Mianyang, Sichuan 621000, China

Received 29 November 2012; Revised 31 January 2013; Accepted 3 February 2013

Academic Editor: Baodong Zheng

Copyright © 2013 Furong Zhao and Jian Chen. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We show the existence of spatial central configurations for the -body problems. In the -body problems, N bodies are at the vertices of a regular N-gon T ; 2p bodies are symmetric with respect to the center of T, and located on the straight line which is perpendicular to the regular N-gon T and passes through the center of T; the th is located at the the center of T. The masses located on the vertices of the regular N-gon are assumed to be equal; the masses located on the same line and symmetric with respect to the center of T are equal.