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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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On the distribution of mass in collinear central configurations
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by Peter W. Lindstrom PDF
Trans. Amer. Math. Soc. 350 (1998), 2487-2523 Request permission

Abstract:

Moulton’s Theorem says that given an ordering of masses, $m_1,m_2, \dotsc ,m_n$, 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.
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): October 1, 1995
  • Received by editor(s) in revised form: September 20, 1996
  • © Copyright 1998 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 350 (1998), 2487-2523
  • MSC (1991): Primary 70F10
  • DOI: https://doi.org/10.1090/S0002-9947-98-01964-3
  • MathSciNet review: 1422613