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 Tools annual

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 Tools monthly

Global: Zendy Plus monthly

Presents the access of premium content as premium feature

Premium Content

Global: Zendy Plus annual

Global: Zendy Free Plan

In the current study, the existence of periodic orbits around a fixedhomogeneous cube is investigated, and the results have powerful implicationsfor examining periodic orbits around non-spherical celestial bodies. In the twodifferent types of symmetry planes of the fixed cube, periodic orbits areobtained using the method of the Poincar\'e surface of section. While ingeneral positions, periodic orbits are found by the homotopy method. Theresults show that periodic orbits exist extensively in symmetry planes of thefixed cube, and also exist near asymmetry planes that contain the regular Hexcross section. The stability of these periodic orbits is determined on thebasis of the eigenvalues of the monodromy matrix. This paper proves that thehomotopy method is effective to find periodic orbits in the gravity field ofthe cube, which provides a new thought of searching for periodic orbits aroundnon-spherical celestial bodies. The investigation of orbits around the cubecould be considered as the first step of the complicated cases, and helps tounderstand the dynamics of orbits around bodies with complicated shapes. Thework is an extension of the previous research work about the dynamics of orbitsaround some simple shaped bodies, including a straight segment, a circularring, an annulus disk, and simple planar plates.

Periodic orbits in the gravity field of a fixed homogeneous cube