We prove that a fixed configuration of N - 1 masses in the plane can be extended to a central configuration of N masses by adding a specified additional mass only in finitely many ways. This holds for a family of potential functions including the Newtonian gravitational case and the classical planar point vortex model.
Bibliographical notePublisher Copyright:
© American Institute of Mathematical Sciences
- Celestial mechanics
- Central configurations
- N-body problem
- Relative equilibria