Classifying four-body convex central configurations
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, orthodi...
| Authors: | , , |
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| Format: | article |
| Publication Date: | 2019 |
| Country: | España |
| Institution: | Universitat Autònoma de Barcelona |
| Repository: | Dipòsit Digital de Documents de la UAB |
| Language: | English |
| OAI Identifier: | oai:ddd.uab.cat:236637 |
| Online Access: | https://ddd.uab.cat/record/236637 https://dx.doi.org/urn:doi:10.1007/s10569-019-9911-7 |
| Access Level: | Open access |
| Keyword: | Central configuration N-Body problem Convex central configurations |
| 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 R+3. |
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