Families of three-dimensional periodic solutions in the circular restricted four-body problem

In this paper we study the 3D symmetric periodic orbits of the circular restricted four-body problem, through their bifurcation from plane orbits. To this end, we calculate the special generating planar periodic orbits, i.e. the vertical-critical orbits, from five basic planar families of symmetric...

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Bibliographic Details
Published in:Astrophysics and space science 2016-04, Vol.361 (4), p.1, Article 129
Main Author: Papadakis, K. E.
Format: Article
Language:English
Subjects:
Astrobiology
Astronomy
Astrophysics
Astrophysics and Astroparticles
Cosmology
Mathematical models
Observations and Techniques
Orbits
Original Article
Physics
Physics and Astronomy
Space Exploration and Astronautics
Space Sciences (including Extraterrestrial Physics
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Summary:In this paper we study the 3D symmetric periodic orbits of the circular restricted four-body problem, through their bifurcation from plane orbits. To this end, we calculate the special generating planar periodic orbits, i.e. the vertical-critical orbits, from five basic planar families of symmetric periodic orbits of the problem. We study the simplest 3D periodic orbits and so we restrict our calculations to simple vertical bifurcation orbits leading to families of one or two revolutions three-dimensional symmetric periodic orbits. We found 21 such families of simple 3D symmetric periodic orbits and typical orbits of all symmetry type 3D orbits are presented. The stability of each calculated 3D periodic orbit is also studied. Characteristic curves as well as stability diagrams of families of 3D periodic orbits are illustrated.
ISSN:0004-640X
1572-946X
DOI:10.1007/s10509-016-2713-4