Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
1895948 | Physica D: Nonlinear Phenomena | 2014 | 4 Pages |
Abstract
For a class of potential functions including those used for the planar n-body and n-vortex problems, we investigate co-circular central configurations whose center of mass coincides with the center of the circle containing the bodies. Useful equations are derived that completely describe the problem. Using a topological approach, it is shown that for any choice of positive masses (or circulations), if such a central configuration exists, then it is unique. It quickly follows that if the masses are all equal, then the only solution is the regular n-gon. For the planar n-vortex problem and any choice of the vorticities, we show that the only possible co-circular central configuration with center of vorticity at the center of the circle is the regular n-gon with equal vorticities.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Applied Mathematics
Authors
Josep M. Cors, Glen R. Hall, Gareth E. Roberts,