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

 

Noncollision singularities in the four-body problem


Author: Robert Orrin Shelton
Journal: Trans. Amer. Math. Soc. 249 (1979), 225-259
MSC: Primary 70F10; Secondary 58E05, 58F05
MathSciNet review: 525672
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Abstract: It is shown that if there is a singularity in a solution of the four-body problem which is not a collision then the motion of the bodies near the singularity is nearly one-dimensional. This is established by grouping the bodies into natural clusters and showing the angular momentum of each cluster with respect to its center of mass tends to zero near the singularity. This is related to Sperling's proof of von Zeipel's theorem.


References [Enhancements On Off] (What's this?)

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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1979-0525672-6
PII: S 0002-9947(1979)0525672-6
Article copyright: © Copyright 1979 American Mathematical Society