Triangle Exact Solution of 3-Bodies Problem

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.

Comments: 9 pages.

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Submission history

[v1] 30 Aug 2011
[v2] 10 Sep 2011
[v3] 13 Sep 2011

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