Abstract
The regularization of the equations of motion of the planar circular restricted three-body problem is considered. The regularization is performed in the canonical variables in the movable coordinate system. Two different L-matrices of the second order are used in the regularization. The constructed equations have a polynomial structure. The obtained system is numerically integrated by the Runge—Kutta—Felberg method. The results of numerical experiments with the parameters of the Earth—Moon system are presented for various L-matrices.
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References
Subbotin, M.F., Vvedenie v teoreticheskuyu astronomiyu (Introduction into the Theoretical Astronomy), Moscow: Nauka, 1968.
Egorov, V.A., Prostranstvennaya zadacha dostizheniya Luny (Spatial Problem of Reaching the Moon), Moscow: Nauka, 1965.
Markeev, A.P., Tochki libratsii v nebesnoi mekhanike i kosmodinamike (Libration Points in the Celestial Mechanics and Cosmodynamics), Moscow: Nauka, 1978.
Szebehely, V., Theory of Orbits in the Restricted Problem of Three Bodies, New York: Academic Press, 1967.
Bruno, A.D., Ogranichennaya zadacha trekh tel: Ploskie periodicheskie orbity (Restricted Three-body Problem: Plane Periodic Orbits), Moscow: Nauka, 1990.
Demin, V.G., Dvizhenie iskusstvennogo sputnika v netsentral’nom pole tyagoteniya (The Motion of an Artificial Satellite in the Non-central Gravitational Field, Moscow: Nauka, 1968.
Heggie, D., A global regularization of the gravitational N-body problem, Celestial Mech., 1974, vol. 10, pp. 217–241.
Aarseth, S. and Zare, K., A regularization of the Three-body problem, Celestial Mech., 1974, vol. 10, pp. 185–205.
Mikkola, S. and Aarseth, S., A chain regularization method for the few-body problem, Celestial Mech., 1990, vol. 47, pp. 375–390.
Poleshchikov, S.M. and Kholopov, A.A., Teoriya L-matrits i regulyarizatsiya uravnenii dvizheniya v nebesnoi mekhanike (Theory of L-matrices and Regularization of the Equations of Motion in the Celestial Mechanics), Syktyvkar: SLI, 1999.
Poleshchikov, S.M., Regularization of the equations of motion with L-transformation and numerical integration of the regular equations, Celest. Mech. and Dyn. Astr., 2003, vol. 85, no. 4, pp. 341–393.
Broucke, R. and Lass, H., A note on relative motion in the general three-body problem, Celestial Mech., 1973, vol. 8, pp. 5–10.
Stepanov, V.V., Kurs differentsial’nykh uravnenii (A Course of Differential Equations), Moscow: GITTL, 1953.
Poleshchikov, S.M., One integrable case of the perturbed two-body problem, Cosmic Res., 2004, vol. 42, no. 4, pp. 398–407.
Poleshchikov, S.M., The motion of a particle in the perturbed field of an attracting center, Cosmic Res., 2007, vol. 45, no. 6, pp. 493–505.
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Original Russian Text © S.M. Poleshchikov, 2015, published in Kosmicheskie Issledovaniya, 2015, Vol. 53, No. 5, pp. 421–429.
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Poleshchikov, S.M. Regularization of equations of the planar restricted problem of three bodies with L-transformations. Cosmic Res 53, 385–393 (2015). https://doi.org/10.1134/S0010952515040061
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DOI: https://doi.org/10.1134/S0010952515040061