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

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References

[1] S. P. Sosnitskii, “On the Lagrange Stability of the Motion for the Three-Body Problem,” Ukrainian Mathematical Journal, Vol. 57, No. 8, 2005, pp. 1341-1349.

[2] E. T. Whittaker, “A Treatise on the Analytical Dynamics of Particles and Rigid Bodies,” Dover, New York, 1944.

[3] G. N. Duboshin, “Celestial Mechanics. Analitical and Qualitative Methods,” Nauka, Moscow, 1964.

[4] L. A. Pars, “A Treatise on Analytical Dynamics,” Heinemann, London, 1965.

[5] V. I. Arnold, “Proof of a Theorem by A. N. Kolmogorov on the invariance of quasiperiodic motions under small perturbations of the Hamiltonian,” Uspekhi Matematicheskikh Nauk, Vol. 18, No. 5, 1963, pp. 13-40.

[6] S. P. Sosnitskii, “On the Orbital Stability of Triangular Lagrangian Motions in the Three-Body Problem,” Astronomical Journal, Vol. 136, No. 6, 2008, pp. 2533-2540.
doi:10.1088/0004-6256/136/6/2533

[7] A. E. Roy, “Orbital Motion,” Adam Hilger LTD, Bristol, 1978.

[8] V. I. Arnold, V. V. Kozlov and A. I. Neishtadt, “Mathematical Aspects of Classical and Celestial Mechanics,” URSS, Moscow, 2002.

[9] V. G. Golubev and E. A. Grebenikov, “The Three-Body Problem in the Celestial Mechanics,” Moscow Univ. Publ., Moscow, 1985.

[10] C. Marchal, “The Three-Body Problem,” Elsevier, Oxford, 1990.

[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.