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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

The number of planar central configurations is finite when $N-1$ mass positions are fixed


Author: Peter W. Lindstrom
Journal: Trans. Amer. Math. Soc. 353 (2001), 291-311
MSC (2000): Primary 70F10
Published electronically: September 18, 2000
MathSciNet review: 1695029
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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.


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Additional Information

Peter W. Lindstrom
Affiliation: Department of Mathematics, Saint Anselm College, Manchester, New Hampshire 03102

DOI: http://dx.doi.org/10.1090/S0002-9947-00-02568-X
PII: S 0002-9947(00)02568-X
Received by editor(s): December 18, 1998
Published electronically: September 18, 2000
Article copyright: © Copyright 2000 American Mathematical Society