The Expansion of the Hamiltonian of the Planetary Problem into the Poisson Series in All Keplerian Elements (Theory) / Kholshevnikov K.V., Greb A.V., Kuznetsov E.D. // Solar System Research. - 2001. - V. 35, l. 3. - P. 243-248.

ISSN:

00380946

Type:

Article

Abstract:

The study of the evolution of planetary systems, primarily of the Solar System, is one of the basic problems of celestial mechanics. The stability of motion of giant planets on cosmogonic time scales was established by numerical and analytical methods, but the question about the evolution of orbits of terrestrial planets and arbitrary solar-type planetary systems remained open. This work initiates a series of papers allowing one to advance in solving the problem of the evolution of the solar-type planetary systems on cosmogonic time scales by using powerful analytical tools. In the first paper of this series, we choose the optimum reference system and obtain the Poisson series expansion of the Hamiltonian of the problem in all Keplerian elements. We propose to use the integral representation of the corresponding coefficients or the Poisson processor means instead of conventionally addressing any possible special functions. This approach extremely simplifies the algorithm. The next paper of this series deals with the calculation of the expansion coefficients.

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нет данных

DOI:

10.1023/A:1010487107989

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https://www.scopus.com/inward/record.uri?eid=2-s2.0-0035617968&doi=10.1023%2fA%3a1010487107989&partnerID=40&md5=b34b133d1b9de1652efc051fa78d234a

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Link	https://www.scopus.com/inward/record.uri?eid=2-s2.0-0035617968&doi=10.1023%2fA%3a1010487107989&partnerID=40&md5=b34b133d1b9de1652efc051fa78d234a
Affiliations	Astronomical Institute, St. Petersburg State University, Bibliotechnaya pl. 2, Petrodvorets, 198904, Russian Federation; Ural State University, ul. Lenina 51, Yekaterinburg, 620083, Russian Federation
References	Duriez, L., Théorème de Poisson en variables héliocentriques (1978) Astron. Astrophys., 68, pp. 182-194; Ito, T., Tanikawa, K., Long-Term Stability of Our Solar System (2000) Proc. 32nd Symp. Celest. Mech., pp. 47-96. , Hayama, Kanagawa (Japan); Ivanova, T.V., Poisson Series Processor PSP (1997) Preprint of Inst. Theor. Astron., Russ. Acad. Sci., (64). , St. Petersburg; Kholshevnikov, K.V., The Convergence of Classical Expansions in Celestial Mechanics (1984) Astron. Zh., 61 (3), pp. 556-563; Kholshevnikov, K.V., (1985) Asimptoticheskie Metody Nebesnoi Mekhaniki, , (Asymptotic Methods in Celestial Mechanics), Leningrad: Leningrad. Gos. Univ; Kholshevnikov, K.V., Conservation of the Shape of Integrals of Areas upon Averaging Transformations (1991) Astron. Zh., 68 (3), pp. 660-663; Kholshevnikov, K.V., Tublina, O.K., Keplerian Coordinates as D' Alamberian Functions (1998) Astron. Zh., 75 (3), pp. 476-480; Kholshevnikov, K.V., Greb, A.V., (2000) Poisson Brackets in Keplerian Elements, (1), pp. 149-153. , Vestn. St. Peterburg. Univ., ser. 1; Kholshevnikova, O.K., (1989) Stability of Planar Circular Orbits of the Averaged Planetary Problem, (2), pp. 108-109. , Vestn. Leningr. Univ., ser. 1; Kinoshita, H., Nakai, H., Long-Term Behavior of the Motion of Pluto over 5.5 Billion Years (1996) Earth, Moon, Planets, 72, pp. 165-173; Laskar, J., Large-Scale Chaos and Marginal Stability in the Solar System (1996) Celest. Mech. Dyn. Astron., 64 (2), pp. 115-162; Nacozy, P., On the Stability of the Solar System (1976) Astron. J., 81 (9), pp. 787-791; Poincaré, A., (1965) Lektsii Po Nebesnoi Mekhanike (Lectures on Celestial Mechanics), , Moscow: Nauka; Sharlier, K., (1966) Nebesnaya Mekhanika (Celestial Mechanics), , Moscow: Nauka; Sokolov, L.L., Kholshevnikov, K.V., On the Representability of Solutions of the Three-Body Problem by Conditionally-Periodic Functions. I, II (1980) Astron. Zh., 57 (1), pp. 168-177; Astron. Zh., (2), pp. 388-396; Subbotin, M.F., (1968) Vvedenie v Teoreticheskuyu Astronomiyu (An Introduction into Theoretical Astronomy), , Moscow: Nauka; Sussman, G.J., Wisdom, J., Chaotic Evolution of the Solar System (1992) Science, 257, p. 56
Correspondence Address	Kholshevnikov, K.V.; Astronomical Institute, St. Petersburg State University, Bibliotechnaya pl. 2, Petrodvorets, 198904, Russian Federation
Language of Original Document	English
Abbreviated Source Title	Sol. Syst. Res.
Source	Scopus