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arXiv · 2004.09797

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

Emese Kővári·Bálint Érdi
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Abstract

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.

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Emese Kővári, Bálint Érdi. 2020-04-21. The Axisymmetric Central Configurations of the Four-Body Problem with Three Equal Masses. https://doi.org/10.3390/sym12040648

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