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

 

On the distribution of mass
in collinear central configurations


Author: Peter W. Lindstrom
Journal: Trans. Amer. Math. Soc. 350 (1998), 2487-2523
MSC (1991): Primary 70F10
MathSciNet review: 1422613
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Abstract: Moulton's Theorem says that given an ordering of masses, $m_1,m_2, \break \dotsc,m_n$, there exists a unique collinear central configuration with center of mass at the origin and moment of inertia equal to 1. This theorem allows us to ask the questions: What is the distribution of mass in this standardized collinear central configuration? What is the behavior of the distribution as $n\to\infty$? In this paper, we define continuous configurations, prove a continuous version of Moulton's Theorem, and then, in the spirit of limit theorems in probability theory, prove that as $n\to\infty$, under rather general conditions, the discrete mass distributions of the standardized collinear central configurations have distribution functions which converge uniformly to the distribution function of the unique continuous standardized collinear central configuration which we determine.


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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/S0002-9947-98-01964-3
PII: S 0002-9947(98)01964-3
Received by editor(s): October 1, 1995
Received by editor(s) in revised form: September 20, 1996
Article copyright: © Copyright 1998 American Mathematical Society