2012/06/27 by Ronaldo S. S. Vieira, Vieira, Ronaldo S. S., Javier Ramos-Caro +1 · 2 citations
Earth and Planetary Sciences · Engineering · Mathematics · Physics and Astronomy · #Astrophysics and Star Formation Studies #Cosmology and Nongalactic Astrophysics (astro-ph.CO) #FOS: Physical sciences #Geophysics and Gravity Measurements #Mathematical Physics (math-ph) #Quantum chaos and dynamical systems #Scientific Research and Discoveries #Spacecraft Dynamics and Control #Stellar, planetary, and galactic studies #astro-ph.CO #math-ph #math.MP
paper · pdf · doi:10.48550/arxiv.1206.6501
18 pages, 9 figures
openalex publication_date 2012/06/27 · arxiv created 2013/04/25 · arxiv updated 2013/04/26 · openalex created_date 2022/08/31 · openalex updated_date 2026/07/28
We make a revision of the stability criteria for equatorial circular orbits, obtained from the epicyclic approximation, which is widely used in Newtonian models for axisymmetric galaxies. We find that, for the case of thin disk models, the criteria of vertical stability must be reformulated, due to the discontinuity in the gravitational field. We show that, for a model characterized by a surface mass density Σ, the necessary and sufficient condition to have vertically stable orbits is that Σ>0. On the other hand, the criteria for radial stability is the same as in thick diks, i.e. that the epicyclic frequency is positive.