Four-body co-circular central configurations
We classify the set of central configurations lying on a common circle in the Newtonian four-body problem. Using mutual distances as coordinates, we show that the set of four-body co-circular central configurations with positive masses is a two-dimensional surface, a graph over two of the exterior s...
| Authors: | , |
|---|---|
| Format: | article |
| Publication Date: | 2012 |
| Country: | España |
| Institution: | Universitat Politècnica de Catalunya (UPC) |
| Repository: | UPCommons. Portal del coneixement obert de la UPC |
| Language: | English |
| OAI Identifier: | oai:upcommons.upc.edu:2117/21123 |
| Online Access: | https://hdl.handle.net/2117/21123 https://dx.doi.org/10.1088/0951-7715/25/2/343 |
| Access Level: | Open access |
| Keyword: | Many-body problem Celestial mechanics Convex central configurations Relative equilibria Problema dels cossos múltiples Mecànica celest Classificació AMS::70 Mechanics of particles and systems::70F Dynamics of a system of particles, including celestial mechanics Àrees temàtiques de la UPC::Matemàtiques i estadística Àrees temàtiques de la UPC::Enginyeria mecànica |
| Summary: | We classify the set of central configurations lying on a common circle in the Newtonian four-body problem. Using mutual distances as coordinates, we show that the set of four-body co-circular central configurations with positive masses is a two-dimensional surface, a graph over two of the exterior side-lengths. Two symmetric families, the kite and isosceles trapezoid, are investigated extensively. We also prove that a co-circular central configuration requires a specific ordering of the masses and find explicit bounds on the mutual distances. In contrast to the general four-body case, we show that if any two masses of a four-body co-circular central configuration are equal, then the configuration has a line of symmetry. |
|---|