The number of planar central configurations is finite when mass positions are fixed

Author:
Peter W. Lindstrom

Journal:
Trans. Amer. Math. Soc. **353** (2001), 291-311

MSC (2000):
Primary 70F10

DOI:
https://doi.org/10.1090/S0002-9947-00-02568-X

Published electronically:
September 18, 2000

MathSciNet review:
1695029

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Abstract | References | Similar Articles | Additional Information

In this paper, it is proved that for and , if masses are located at fixed points in a plane, then there are only a finite number of -point central configurations that can be generated by positioning a given additional 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.

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Additional Information

**Peter W. Lindstrom**

Affiliation:
Department of Mathematics, Saint Anselm College, Manchester, New Hampshire 03102

DOI:
https://doi.org/10.1090/S0002-9947-00-02568-X

Received by editor(s):
December 18, 1998

Published electronically:
September 18, 2000

Article copyright:
© Copyright 2000
American Mathematical Society