Open AccessOn bifurcations and stability of central configurations in the planar circular restricted four-body problem
Author(s) -
B. S. Bardin,
Е. В. Волков
Publication year - 2021
Publication title -
journal of physics. conference series
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.21
H-Index - 85
eISSN - 1742-6596
pISSN - 1742-6588
DOI - 10.1088/1742-6596/1959/1/012006
Subject(s) - equilateral triangle , three body problem , plane (geometry) , classical mechanics , planar , physics , stability (learning theory) , particle (ecology) , newtonian fluid , center of mass (relativistic) , circular orbit , motion (physics) , celestial mechanics , geometry , mathematics , mathematical analysis , oceanography , computer graphics (images) , energy–momentum relation , machine learning , computer science , geology
The restricted four-body problem is considered. That is, we consider motion of an infinitely small body (particle) under the Newtonian gravitational attraction of three bodies (primaries). It is assumed that the primaries move in circular orbits, forming a stable equilateral Lagrange triangle. It is supposed that four bodies move in a plane. There exist relative equilibriums of the particle in the rotating with the primaries coordinate system. In such an equilibrium the particle forms a central configuration with the primaries. In the case of small mass ofa primary the bifurcations ofthe central configurations are investigated, as well as conditions oflinear stability for the central configurations is obtained. The study is performed analytically by using small parameter method.