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Central configurations of the 4-body problem with masses m1 ¼ m2 > m3 ¼ m4 ¼ m > 0 and m small

Central configurations of the 4-body problem with masses m1 ¼ m2 > m3 ¼ m4 ¼ m > 0 and m small
 
Corbera Subirana, Montserrat ; Llibre, Jaume
2014

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Enllaç permanent: http://hdl.handle.net/10854/3747
 
Versió de l'editor: https://doi.org/10.1016/j.amc.2014.07.109
 

Resumen

In this paper we give a complete description of the families of central configurations of the planar 4-body problem with two pairs of equals masses and two equal masses sufficiently small. In particular, we give an analytical proof that this particular 4-body problem has exactly 34 different classes of central configurations. ...»»»»
In this paper we give a complete description of the families of central configurations of the planar 4-body problem with two pairs of equals masses and two equal masses sufficiently small. In particular, we give an analytical proof that this particular 4-body problem has exactly 34 different classes of central configurations. Moreover for this problem we prove the following two conjectures: There is a unique convex planar central configuration of the 4-body problem for each ordering of the masses in the boundary of its convex hull, which appears in Albouy and Fu (2007) [3]. We also prove the conjecture: There is a unique convex planar central configuration having two pairs of equal masses located at the adjacent vertices of the configuration and it is an isosceles trapezoid. Finally, the families of central configurations of this 4-body problem are numerically continued to the 4-body problem with four equal masses.^^^^

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Artículo

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Indexat a WOS/JCR

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(c) 2014 Elsevier. Published article is available at: http://dx.doi.org/10.1016/j.amc.2014.07.109

Citación Bibliográfica:

Corbera Subirana, M., & Llibre, J. (2014). Central configurations of the 4-body problem with masses m(1) = m(2) > m(3) = m(4) = m > 0 and m small. Applied Mathematics and Computation, 246, 121-147.