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Advances in Mathematical Physics
Volume 2014, Article ID 478495, 3 pages
Research Article

On a Periodic Solution of the 4-Body Problems

1Mathematical College, Sichuan University, Chengdu, Sichuan 610064, China
2School of Science, Southwest University of Science and Technology, Mianyang, Sichuan 621010, China

Received 25 November 2013; Accepted 6 January 2014; Published 11 February 2014

Academic Editor: Dongho Chae

Copyright © 2014 Jian Chen and Bingyu Li. 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 necessary and sufficient conditions on the masses for the periodic solution of planar 4-body problems, where three particles locate at the vertices of an equilateral triangle and rotate with constant angular velocity about a resting particle. We prove that the above periodic motion is a solution of Newtonian 4-body problems if and only if the resting particle is at the origin and the masses of the other three particles are equal and their angular velocity satisfies a special condition.