Number of central configurations and singular surfaces in the mass space in the collinear four-body problem (Q2884391)
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scientific article; zbMATH DE number 6038803
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Number of central configurations and singular surfaces in the mass space in the collinear four-body problem |
scientific article; zbMATH DE number 6038803 |
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Number of central configurations and singular surfaces in the mass space in the collinear four-body problem (English)
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29 May 2012
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central configurations
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\(N\)-body problem
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geometric equivalence
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permutation equivalence
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mass equivalence
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singular surfaces
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0.93125486
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0.90351695
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0.8982668
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0.8959064
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0.8915436
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0.8908871
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The authors consider the problem of the number of collinear central configurations in the \(N\)-body problem, where the \(N\) bodies are located on the \(x\)-axis. For any given mass vector, the problem is to determine the number of geometric equivalence classes of the \(N\)-body collinear central configurations, where two configurations are said to be geometrically equivalent if they are similar modulo translations, dilations, rotations and permutations. It is shown that there exists a parametric surface in the mass space, which decreases the total number of collinear central configurations. Within this set and for mutually distinct masses the number of central configurations is 11.
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