The Axisymmetric Central Configurations of the Four-Body Problem with Three Equal Masses

Symmetry

Emese Kővári¹  Bálint Érdi¹ 

[1] Department of Astronomy, Eötvös Loránd University, Pázmány Péter Sétány 1/A, 1117 Budapest, Hungary;

关键词: celestial mechanics;    four-body problem;    central configurations;   

DOI  :  10.3390/sym12040648

来源: DOAJ

【 摘 要 】

In the studied axisymmetric case of the central four-body problem, the axis of symmetry is defined by two unequal-mass bodies, while the other two bodies are situated symmetrically with respect to this axis and have equal masses. Here, we consider a special case of the problem and assume that three of the masses are equal. Using a recently found analytical solution of the general case, we formulate the equations of condition for three equal masses analytically and solve them numerically. A complete description of the problem is given by providing both the coordinates and masses of the bodies. We show furthermore how the three-equal-mass solutions are related to the general case in the coordinate space. The physical aspects of the configurations are also studied and discussed.

【 授权许可】

Unknown