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Journal of Applied Mathematics
Volume 2013 (2013), Article ID 315976, 6 pages
Research Article

Spatial Central Configurations with Two Twisted Regular 4-Gons

1School of Electronic Engineering, UEST Of China, Chengdu 610054, China
2Department of Mathematics, Yibin University, Sichuan, 644007, China
3Department of Mathematics and Computer Science, Mianyang Normal University, Mianyang, Sichuan 621000, China

Received 23 May 2013; Accepted 19 September 2013

Academic Editor: Orazio Descalzi

Copyright © 2013 Sen Zhang and Furong Zhao. 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.


We study the configuration formed by two squares in two parallel layers separated by a distance. We picture the two layers horizontally with the -axis passing through the centers of the two squares. The masses located on the vertices of each square are equal, but we do not assume that the masses of the top square are equal to the masses of the bottom square. We prove that the above configuration of two squares forms a central configuration if and only if the twist angle is equal to or () .