AM  Vol.4 No.2 , February 2013
On the Lagrange Stability of Motion and Final Evolutions in the Three-Body Problem
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 [1], which band together separately squared mutual distances between bodies (mass points) and squared 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.


Cite this paper
S. Sosnitskii, "On the Lagrange Stability of Motion and Final Evolutions in the Three-Body Problem," Applied Mathematics, Vol. 4 No. 2, 2013, pp. 369-377. doi: 10.4236/am.2013.42057.
References
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[11]   L. G. Luk’yanov and G. I. Shirmin, “Sundman Surfaces and Hill Stability in the Three-Body Problem,” Letters to the Astronomical Journal, Vol. 33, No. 8, 2007, pp. 618-630.

[12]   S. P. Sosnitskii, “On the Lagrange and Hill Stability of the Motion of Certain Systems with Newtonian Potential,” Astronomical Journal, Vol. 117, No. 6, 1999, pp. 3054-3058. doi:10.1086/300889

[13]   J. Chazy, “Sur l’Allure Finale Mouvement dans le Probleme des Trois Corps Quand le Temps Croit Indefiniment,” Annales de l’Ecole Normale Superieure, 3eme Serie, Vol. 39, 1922, pp. 29-130.

 
 
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