### Abstract

We characterize the planar Central configurations of the 4-body problem with masses m1=m2≠m3=m4 which have an axis of symmetry. It is known that this problem has exactly two classes of convex Central configurations, one with the shape of a rhombus and the other with the shape of an isosceles trapezoid. We show that this 4-body problem also has exactly two classes of concave Central configurations with the shape of a kite, this proof is assisted by computer. © 2012 Elsevier Inc. All rights reserved.

Original language | English |
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Pages (from-to) | 5996-6001 |

Journal | Applied Mathematics and Computation |

Volume | 219 |

Issue number | 11 |

DOIs | |

Publication status | Published - 29 Jan 2013 |

### Keywords

- 4-Body problem
- Central configuration
- Convex and concave central configurations

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## Cite this

Alvarez-Ramírez, M., & Llibre, J. (2013). The symmetric central configurations of the 4-body problem with masses m<inf>1</inf> = m<inf>2</inf> ≠ m<inf>3</inf> = m<inf>4</inf>

*Applied Mathematics and Computation*,*219*(11), 5996-6001. https://doi.org/10.1016/j.amc.2012.12.036