References
A. D. Bryuno,Local Method for Nonlinear Analysis of Differential Equations [in Russian], Nauka, Moscow (1979).
S. Yu. Sadov, “Analysis of the function that determines the rotation stability of a nearly symmetric satellite,”Preprint of the Institute of Applied Mathematics,84 (1994).
S. Yu. Sadov, “Coefficients of the averaged satellite oscillation equation,”Preprint of the Institute of Applied Mathematics,27 (1995).
V. V. Beletskii, “On the libration of a satellite,” in:Artificial Earth Satellites [in Russian], Vol. 3, Izd. AN SSSR, Moscow (1959), pp. 13–31.
F. L. Chernous'ko,Zh. Vychisl. Mat. i Mat. Fiz. [U.S.S.R. Comput. Math. and Math. Phys.],3, No. 3, 528–538 (1963).
A. D. Bryuno, “Oscillation of a satellite in an elliptic orbit,”Preprint of the Institute of Applied Mathematics,18 (1976).
A. D. Bryuno,Mat. Zametki [Math. Notes],22, No. 1, 109–116 (1977).
F. H. Lutze, Jr. and M. W. Abbit, Jr.,Celest. Mech.,1, No. 1, 31–35 (1969).
V. A. Sarychev,Orientation of Artificial Satellites [in Russian], in:Investigations of Outer Space, Itogi Nauki i Tekhniki, Vol. 11, VINITI, Moscow (1978).
V. A. Sarychev, V. A. Zlatoustov, and V. V. Sazonov,Numerical Study of Periodic Solutions to Second-Order Differential Equations [in Russian], Dep. VINITI No. 908-77, Moscow (1977).
A. D. Bryuno and V. Yu. Petrovich, “Regularization of the oscillation of a satellite in a highly elongated orbit,”Preprint of the Institute of Applied Mathematics,4 (1994).
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Translated fromMatematicheskie Zametki, Vol. 58, No. 5, pp. 785–789, November, 1995.
I wish to express gratitude to A. D. Bryuno for posing the problem and discussing the results.
This research was supported by the International Science Foundation under grant No. M3W300.
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Sadov, S.Y. Normal form of the satellite oscillation equation in the singular case. Math Notes 58, 1234–1237 (1995). https://doi.org/10.1007/BF02305009
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DOI: https://doi.org/10.1007/BF02305009