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- W4293407274 abstract "In this paper we characterize all the solutions of the three body problem on which one body with mass $m_1$ remains in a fixed line and the other two bodies have the same mass $m_2$. We show that all the solutions with negative total energy (potential plus kinetic), never collide. Explicit solutions of the motion of all the three bodies are given in term of just one solution of an ordinary differential equation of order two of one real value function. We show that the solutions of a big subfamily of this family remains bounded for all time. The same results are shown for the n-body problem. When the body on the line remains constant, we have provide exact formulas for the solutions --for any n-- in the same way as we have for the two body problem. Once we have shown that there are infinitely many periodic solutions, we provide several examples of periodic examples for the 3-Body, 4-Body, 5-Body and 6-Body problem. This is a first version. Comments and suggestions for references are welcome. A YouTube video explaining one of this solutions has been posted on http://youtu.be/2Wpv6vpOxXk" @default.
- W4293407274 created "2022-08-29" @default.
- W4293407274 creator A5024135704 @default.
- W4293407274 date "2014-10-07" @default.
- W4293407274 modified "2023-10-18" @default.
- W4293407274 title "A family of Solutions of the N-Body Problem" @default.
- W4293407274 doi "https://doi.org/10.48550/arxiv.1410.1757" @default.
- W4293407274 hasPublicationYear "2014" @default.
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