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/

Zendy Plus

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

Zendy Tools

Zendy Open

We consider the motion of point masses given by a natural extension ofNewtonian gravitation to spaces of constant positive curvature. Our goal is toexplore the spectral stability of tetrahedral orbits of the corresponding4-body problem in the 2-dimensional case, a situation that can be reduced tostudying the motion of the bodies on the unit sphere. We first perform someextensive and highly precise numerical experiments to find the likely regionsof stability and instability, relative to the values of the masses and to thelatitude of the position of three equal masses. Then we support the numericalevidence with rigorous analytic proofs in the vicinity of some limit cases inwhich certain masses are either very large or negligible, or the latitude isclose to zero.

On the stability of tetrahedral relative equilibria in the positively curved 4-body problem