Classifying four-body convex central configurations. (English) Zbl 1451.70022
Summary: We classify the full set of convex central configurations in the Newtonian planar 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 \(\mathbb{R}^{+^3}\).
MSC:
| 70F10 | \(n\)-body problems |
| 70F15 | Celestial mechanics |
| 70G10 | Generalized coordinates; event, impulse-energy, configuration, state, or phase space for problems in mechanics |
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