The number of planar central configurations is finite when $N-1$ mass positions are fixed
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- by Peter W. Lindstrom PDF
- Trans. Amer. Math. Soc. 353 (2001), 291-311 Request permission
Abstract:
In this paper, it is proved that for $n>2$ and $n\not =4$, if $n-1$ masses are located at fixed points in a plane, then there are only a finite number of $n$-point central configurations that can be generated by positioning a given additional $n$th mass in the same plane. The result is established by proving an equivalent isolation result for planar central configurations of five or more points. Other general properties of central configurations are established in the process. These relate to the amount of centrality lost when a point mass is perturbed and to derivatives associated with central configurations.References
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Additional Information
- Peter W. Lindstrom
- Affiliation: Department of Mathematics, Saint Anselm College, Manchester, New Hampshire 03102
- Received by editor(s): December 18, 1998
- Published electronically: September 18, 2000
- © Copyright 2000 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 353 (2001), 291-311
- MSC (2000): Primary 70F10
- DOI: https://doi.org/10.1090/S0002-9947-00-02568-X
- MathSciNet review: 1695029