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Existence and linear stability of the rhomboidal periodic orbit in the planar equal mass four-body problem
- Source :
-
Journal of Mathematical Analysis & Applications . Apr2012, Vol. 388 Issue 2, p942-951. 10p. - Publication Year :
- 2012
-
Abstract
- Abstract: In this paper, we study the existence and linear stability of the rhomboidal periodic orbit in the planar equal mass four-body problem. The Hamiltonian of the differential system is regularized by a Levi–Civita type transformation and an appropriate scaling of time. The initial condition of this orbit is shown to be the infimum of some well-chosen set. This existence proof is direct and surprisingly simple. Further, a careful study shows that this orbit has a symmetry group isomorphic to the dihedral group . Then Robertsʼ symmetry reduction method is applied to show the linear stability. It turns out that the rhomboidal periodic orbit in the planar equal mass four-body problem is linearly stable. [Copyright &y& Elsevier]
Details
- Language :
- English
- ISSN :
- 0022247X
- Volume :
- 388
- Issue :
- 2
- Database :
- Academic Search Index
- Journal :
- Journal of Mathematical Analysis & Applications
- Publication Type :
- Academic Journal
- Accession number :
- 70233539
- Full Text :
- https://doi.org/10.1016/j.jmaa.2011.10.032