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Mat. Zametki, 1977, Volume 22, Issue 1, Pages 109–116 (Mi mz8030)  

This article is cited in 2 scientific papers (total in 2 papers)

Properties of certain functions of celestial mechanics

A. D. Bruno

Applied Mathematics Institute, Academy of Sciences of the USSR

Abstract: In [1] the planar motion of a satellite in an elliptic orbit by the Krylov–Bogolyubov asymptotic method is studied. In particular, oscillations of a satellite in an absolute coordinate system are considered. In this case, the terms of the first, second, and fourth orders in the small parameter are trivially equal to zero in the averaged system. In this article, the proofs of nontrivial statements are given for the above-mentioned preprint, and viz., the terms of the third order are also zero and certain coefficients in terms of the fifth order are equal to each other.

Full text: PDF file (406 kB)

English version:
Mathematical Notes, 1977, 22:1, 550–554

Bibliographic databases:

UDC: 517.52
Received: 25.10.1976

Citation: A. D. Bruno, “Properties of certain functions of celestial mechanics”, Mat. Zametki, 22:1 (1977), 109–116; Math. Notes, 22:1 (1977), 550–554

Citation in format AMSBIB
\Bibitem{Bru77}
\by A.~D.~Bruno
\paper Properties of certain functions of celestial mechanics
\jour Mat. Zametki
\yr 1977
\vol 22
\issue 1
\pages 109--116
\mathnet{http://mi.mathnet.ru/mz8030}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=464803}
\zmath{https://zbmath.org/?q=an:0374.70025}
\transl
\jour Math. Notes
\yr 1977
\vol 22
\issue 1
\pages 550--554
\crossref{https://doi.org/10.1007/BF01147698}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. S. Yu. Sadov, “Normal form of the satellite oscillation equation in the singular case”, Math. Notes, 58:5 (1995), 1234–1237  mathnet  crossref  mathscinet  zmath  isi
    2. Sadov, SY, “Averaging of the equation of motion of a satellite with respect to its center of mass in degenerate cases: 1. Oscillations in the absolute frame of reference”, Cosmic Research, 46:2 (2008), 172  crossref  isi
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