Stability of the Rhomboidal Symmetric-Mass Orbit
Dynamical Systems
2013-05-01 v2
Abstract
We study the rhomboidal symmetric-mass 4-body problem in both a two-degree-of-freedom and a four-degree-of-freedom setting. Under suitable changes of variables in both settings, isolated binary collisions at the origin are regularizable. Linear stability analysis is performed in both settings. For the two-degree-of-freedom setting, linear stability is established for a wide interval of mass ratios. A Poincar\'{e} section analysis is also performed, showing stability. In the four-degree-of-freedom setting, linear stability fails except for a very small interval of mass ratios.
Keywords
Cite
@article{arxiv.1208.3183,
title = {Stability of the Rhomboidal Symmetric-Mass Orbit},
author = {Lennard Bakker and Skyler Simmons},
journal= {arXiv preprint arXiv:1208.3183},
year = {2013}
}
Comments
27 pages, 12 figures