## The 3D elliptic restricted three-body problem: periodic orbits which bifurcate from limiting restricted problems## Complex instability
In the present work we use certain isolated symmetric periodic orbits found in some limiting Restricted Three-Body Problems to obtain, by numerical continuation, families of symmetric periodic orbits of the more general Spatial Elliptic Restricted Three Body Problem. In particular, the Planar Isosceles Restricted Three Body Problem, the Sitnikov Problem and the MacMillan problem are considered. A stability study for the periodic orbits of the families obtained - specially focused to detect transitions to complex instability - is also made.
This article contains no SIMBAD objects. ## Contents- 1. Introduction
- 2. The planar isosceles restricted problem
- 2.1. The central family of periodic orbits
- 2.2. Bifurcation branches
- 2.2.1. Remarks
- 2.3. Limiting periodic orbits when
- 2.3.1. Remarks
- 2.4. Periodic orbits in the configuration space
- 3. The spatial elliptic restricted three-body problem with equal masses
- 4. The Sitnikov problem
- 5. Conclusions
- Acknowledgements
- Appendix A: gallery of periodic orbits
- References
© European Southern Observatory (ESO) 1999 Online publication: November 16, 1999 |