An analytical proof on certain determinants connected with the collinear central configurations in the n-body problem |
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Authors: | Zhifu Xie |
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Affiliation: | 1. Department of Mathematics and Computer Science, Virginia State University, Petersburg, VA, 23806, USA
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Abstract: | In this paper we give a short analytical proof of the inequalities proved by Albouy–Moeckel through computer algebra, in the cases $n=5$ and $n=6$ . These inequalities guarantee that, in the $n$ -body problem, the family of mass vectors making a given collinear configuration a central configuration is 2-dimensional. The induction techniques here may be used to prove the inequalities for general $n$ with more subtle estimation but currently the inequalities still remains unproved for $nge 7$ . |
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