Study on the Lagrange Stability of Motion and Final Evolutions in the Three-Body Problem

For the three-body problem, we consider the stability of Lagrange. We use the relationships of the author from[1] to analyze stability, along with integrals of energy and angular momentum, which connect separately squared mutual distances between bodies (mass points) and squared mutual distances from bodies to the system’s barycenter. We are proving the theorem of Lagrange stability, which helps us to define more specifically the character of the final evolutions of hyperbolic-elliptic and parabolic-elliptic.

Aurthor(s) Details:

S. P. Sosnitskii
Institute of Mathematics of Ukrainian National Academy of Sciences, Tereshchenkivs’ka str 3, 01601, MSP, Kyiv–4, Ukraine.

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