On the Lagrange Stability of Motion and final Evolutions in the Three-Body Problem

2012/10/01 by S. P. Sosnitskii, Stepan Sosnitskii, Sosnitskii, Stepan
Engineering · Physics and Astronomy · #70F15 #Astro and Planetary Science #Earth and Planetary Astrophysics (astro-ph.EP) #FOS: Physical sciences #Space Satellite Systems and Control #Spacecraft Dynamics and Control #astro-ph.EP #msc:70F15

paper · pdf · doi:10.48550/arxiv.1210.0321

19 pages

arxiv created 2012/10/01 · openalex publication_date 2012/10/01 · arxiv updated 2012/10/02 · openalex created_date 2025/10/24 · openalex updated_date 2026/07/28

Abstract

For the three-body problem, we consider the Lagrange stability. To analyze the stability, along with integrals of energy and angular momentum, we use relations by the author from Sosnitskii (2005), which band together separately squared mutual distances between bodies (mass points) and squared mutual distances from bodies to the barycenter of the system. In this case, we prove the Lagrange stability theorem, which allows us to define more exactly the character of hyperbolic-elliptic and parabolic-elliptic final evolutions

Citations

• PROOF OF A THEOREM OF A. N. KOLMOGOROV ON THE INVARIANCE OF QUASI-PERIODIC MOTIONS UNDER SMALL PERTURBATIONS OF THE HAMILTONIAN

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