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arXiv · 1903.01684

Classifying Four-Body Convex Central Configurations

Montserrat Corbera·Josep M. Cors·Gareth E. Roberts
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Abstract

We classify the full set of convex central configurations in the Newtonian four-body problem. Particular attention is given to configurations possessing some type of symmetry or defining geometric property. Special cases considered include kite, trapezoidal, co-circular, equidiagonal, orthodiagonal, and bisecting-diagonal configurations. Good coordinates for describing the set are established. We use them to prove that the set of four-body convex central configurations with positive masses is three-dimensional, a graph over a domain $D$ that is the union of elementary regions in $\mathbb{R}^{+^3}$.

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Montserrat Corbera, Josep M. Cors, Gareth E. Roberts. 2019-03-05. Classifying Four-Body Convex Central Configurations. https://doi.org/10.1007/s10569-019-9911-7

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