Abstract
The integrable case of the perturbed two-body problem is considered. The perturbation is determined by the potential of a special form. The L-matrix is chosen in such a way that partial separation of variables should take place in regular coordinates. Integration of the equations of motion of the problem under consideration is made. The solutions are expressed through elliptic functions. The orbits for various cases are constructed. The results of numerical calculations are given.
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Poleshchikov, S.M., One Integrable Case of the Perturbed Two-Body Problem, Kosm. Issled., 2004, vol. 42, no. 4, pp. 414–423.
Beletskii, V.V., Trajectories of Space Flights with Constant Vector of Jet Acceleration, Kosm. Issled., 1964, vol. 2, no. 3, pp. 787–807.
Kunitsyn, A.L., Motion of a Rocket with a Constant Jet Acceleration Vector in the Central Field of Forces, Kosm. Issled., 1966, vol. 4, no. 2, pp. 324–332.
Demin, V.G., Dvizhenie iskusstvennogo sputnika v netsentral’nom pole tyagoteniya (Motion of Artificial Satellite in a Noncentral Gravitational Field), Moscow: Nauka, 1968.
Kirchgraber, U., A Problem of Orbital Dynamics, Which Is Separable in KS-Variables, Celestial Mech., 1971, vol. 4, pp. 340–347.
Poleshchikov, S.M. and Kholopov, A.A., Teoriya L-matrits i regulyarizatsiya uravnenii dvizheniya v nebesnoi mekhanike (The Theory of L-Matrices and Regularization of Equations of Motion in Celestial Mechanics), Syktyvkar: Syktyvkar Inst. of Forestry, 1999.
Poleshchikov, S.M., Regularization of Motion Equations with L-Iransformation and Numerical Integration of the Regular Equations, Celest. Mech. and Dyn. Astr., 2003, vol. 85, no. 4, pp. 341–393.
Poleshchikov, S.M., Regularization of Canonical Equations of the Two-Body Problem Using a Generalized KS-Matrix, Kosm. Issled., 1999, vol. 37, no. 3, pp. 322–328.
Prudnikov, A.P., Brychkov, Yu.A., and Marichev, O.I., Integraly i Ryady (Integrals and Series), Moscow: Nauka, 1981.
Byrd, P.F. and Friedman, M.D., Handbook of Elliptic Integrals for Engineers and Physicists, Berlin: Springer, 1954.
Sikorskii, Yu.S., Elementy teorii ellipticheskikh funktsii s prilozheniyami k mekhanike (Elements of the Theory of Elliptic Functions with Application to Problem of Mechanics), Moscow: ONTI, 1936.
Smirnov, V.I., Kurs vysshei matematiki (A Course of Higher Mathematics), Moscow: Nauka, 1974, vol. 3,part 2.
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Original Russian Text © S.M. Poleshchikov, 2007, published in Kosmicheskie Issledovaniya, 2007, Vol. 45, No. 6, pp. 522–535.