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Existence and stability of symmetric periodic simultaneous binary collision orbits in the planar pairwise symmetric four-body problem.
- Source :
-
Celestial Mechanics & Dynamical Astronomy . Jul2011, Vol. 110 Issue 3, p271-290. 20p. - Publication Year :
- 2011
-
Abstract
- We analytically prove the existence of a symmetric periodic simultaneous binary collision orbit in a regularized planar pairwise symmetric equal mass four-body problem. This is an extension of our previous proof of the analytic existence of a symmetric periodic simultaneous binary collision orbit in a regularized planar fully symmetric equal mass four-body problem. We then use a continuation method to numerically find symmetric periodic simultaneous binary collision orbits in a regularized planar pairwise symmetric 1, m, 1, m four-body problem for m between 0 and 1. Numerical estimates of the the characteristic multipliers show that these periodic orbits are linearly stability when 0.54 ≤ m ≤ 1, and are linearly unstable when 0 < m ≤ 0.53. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 09232958
- Volume :
- 110
- Issue :
- 3
- Database :
- Academic Search Index
- Journal :
- Celestial Mechanics & Dynamical Astronomy
- Publication Type :
- Academic Journal
- Accession number :
- 62662117
- Full Text :
- https://doi.org/10.1007/s10569-011-9358-y