The masses in a symmetric centered solution of the $n$-body problem
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- by Florin Nicolae Diacu PDF
- Proc. Amer. Math. Soc. 109 (1990), 1079-1085 Request permission
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
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Additional Information
- © Copyright 1990 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 109 (1990), 1079-1085
- MSC: Primary 70F10
- DOI: https://doi.org/10.1090/S0002-9939-1990-1010798-3
- MathSciNet review: 1010798