Abstract
In the problem under consideration, the libration points are determined, and their stability is investigated. The surfaces of zero velocity are constructed, and the regions where motion is possible are found. The limiting case of the problem is considered.
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Euler, L., Un Corps Étant Attiré an Raison Réciproque Quarreé des Distances vers Deux Points Fixes Donnés, Mem., Berlin, 1760, vol. 228.
Lagrange, J., Recherches sur le Mouvement d’un Corp’s qui Est Attire par Deux Centres Fixes, Oeuvres de Lagrange, vol. 2, p. 67 or Mem. de Turin, 1766–1769, vol. 4. pp. 118, 215.
Jacobi, C., Lektsii po dinamike (Lectures in Dynamics), Moscow: ONTI, 1936.
Darboux, G., Sur un Problem de Mechanique, Archives Neerlandaises des Sciences. Exact et Naturel, 1901, ser. 2, vol. 6, p. 371.
Aksenov, E.P., Grebenikov, E.A., and Demin, V.G., General Solution to the Problem of Motion of a Satellite in the Normal Field of Attraction of the Earth, Iskusstvennye Sputniki Zemli, 1961, no. 8, p. 64.
Aksenov, E.P., Teoriya dvizheniya iskusstvennykh sputnikov Zemli (The Theory of Motion of the Earth’s Artificial Satellites), Moscow: Nauka, 1977.
Lukyanov, L.G., Surfaces of Zero Velocity in the Restricted Photo-Gravitational Three-Body Problem, Astron. Zh., 1988, vol. 65, p. 422.
Sedov, L.I., Metody podobiya i razmernosti v mekhanike (Similarity and Dimensional Methods in Mechanics), Moscow: Nauka, 1980. Translation of 4th Russ. ed., New York: Academic Press, 1959.
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Original Russian Text © L.G. Lukianov, 2006, published in Kosmicheskie Issledovaniya, 2006, Vol. 44, No. 2, pp. 162–169.
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Lukianov, L.G. Generalized problem of two fixed centers. Cosmic Res 44, 152–159 (2006). https://doi.org/10.1134/S0010952506020079
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DOI: https://doi.org/10.1134/S0010952506020079