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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

The masses in a symmetric centered solution of the $ n$-body problem


Author: Florin Nicolae Diacu
Journal: Proc. Amer. Math. Soc. 109 (1990), 1079-1085
MSC: Primary 70F10
MathSciNet review: 1010798
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Abstract | References | Similar Articles | Additional Information

Abstract: We prove that if a planar solution of the $ n$-body problem has a symmetry axis, fixed with respect to the considered frame, and the center of mass of the particle system lies on this axis during the motion, then the symmetric masses must be equal. We also show that the set of initial conditions leading to symmetric solutions has measure zero and is nowhere dense relative to the set of all initial conditions that define solutions in the space.


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

  • [1] F. N. Diacu, Improbability of collinear solutions in the $ n$-body problem with generalized attraction law, Astron. Nachr. 309 (1988), 233-236. MR 992725 (90c:70015)
  • [2] -, Wintner's collinear and flat solutions are nowhere dense, Celest. Mech. 44 (1988), 261-265. MR 993816 (90c:70016)
  • [3] -, On the planar syzygy solutions of the $ 3$-body problem, Celest. Mech. (to appear).
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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1990-1010798-3
PII: S 0002-9939(1990)1010798-3
Keywords: $ n$-body problem, celestial mechanics, measure, nowhere dense set
Article copyright: © Copyright 1990 American Mathematical Society



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