English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

The study of off-equatorial orbits in razor-thin disks is still in itsbeginnings. Contrary to what was presented in the literature in recentpublications, the vertical stability criterion for equatorial circular orbitscannot be based on the vertical epicyclic frequency, because of thediscontinuity in the gravitational field on the equatorial plane. We present arigorous criterion for the vertical stability of circular orbits in systemscomposed by a razor-thin disk surrounded by a smooth axially symmetricdistribution of matter, the latter representing additional structures such asthick disk, bulge and (dark matter) halo. This criterion is satisfied once themass surface density of the thin disk is positive. Qualitative and quantitativeanalyses of nearly equatorial orbits are presented. In particular, the analysisof nearly equatorial orbits allows us to construct an approximate analyticalthird integral of motion in this region of phase-space, which describes theshape of these orbits in the meridional plane.

On the stability of circular orbits in galactic dynamics: Newtonian thin disks