Authors: Sergey V. Ershkov
Here is presented a system of equations of 3-bodies problem in well-known Lagrange's form (describing a relative motions of 3-bodies). Analyzing of such a system, we obtain an exact solution in special case of constant ratios of relative distances between the bodies. Above simplifying assumption reduces all equations of initial system to a proper similar form, which leads us to a final solution: initial triangle of bodies m1 , m2, m3 is moving as entire construction, simultaneously rotating over the common center of masses as well as increasing or decreasing of it's size proportionally.
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