Expansion of the Hamiltonian of the two-planetary problem into the poisson series in all elements: Application of the poisson series processor / Kuznetsov E.D., Kholshevnikov K.V. // Solar System Research. - 2004. - V. 38, l. 2. - P. 147-154.

ISSN:

00380946

Type:

Review

Abstract:

This paper is the third in a series of articles devoted to one of the basic problems of celestial mechanics: the study of the evolution of solar-type planetary systems. In the previous papers a brief review of the history and current state of the problem was given; the plan of the study was outlined; the Jacobi coordinates and the related osculating elements were introduced; the form of the Poisson expansion of the Hamiltonian in all elements was given; and the expansion coefficients for the Hamiltonian of the two-planetary Sun-Jupiter-Saturn problem were obtained (though with impure accuracy) by a simple algorithm that is reduced to the calculation of multiple integrals of elementary functions. In the present paper the expansion of the Hamiltonian of the two-planetary Sun-Jupiter-Saturn problem into the Poisson series in all elements is constructed with the help of the PSP Poisson series processor, which is capable of required accuracy.

Author keywords:

Index keywords:

нет данных

DOI:

10.1023/B:SOLS.0000022825.9383

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Link	https://www.scopus.com/inward/record.uri?eid=2-s2.0-4043113488&doi=10.1023%2fB%3aSOLS.0000022825.93837.7d&partnerID=40&md5=f94b938cc71cdde6359dece9852400f0
Affiliations	Ural State University, pr. Lenina 51, Yekaterinburg, 620083, Russian Federation; Sobolev Astronomical Institute, St. Petersburg State University, Universitetskii pr. 28, St. Petersburg, 198504, Russian Federation
References	Brumberg, V.A., (1980) Analiticheskie Algoritmy Nebesnoi Mekhaniki (Analytic Algorytms of Celestial Mechanics), , Moscow: Nauka; Ivanova, T.V., Poisson series processor PSP (1997) Preprint of Inst. Theor. Astron., Russ. Akad. Sci., p. 64. , St. Petersburg; Kholshevnikov, K.V., D'Alembertian functions in celestial mechanics (1997) Astron. Zh., 74 (1), pp. 146-153; (1997) Astron. Rep. (Engl. Transl.), 41, pp. 135-142; Kholshevnikov, K.V., Tublina, O.K., Coordinates in keplerian motion as D'Alembertian functions (1998) Astron. Zh., 75 (3), pp. 476-480; (1998) Astron. Rep. (Engl. Transl.), 42, pp. 420-424; Kholshevnikov, K.V., Greb, A.V., Kuznetsov, E.D., The expansion of the Hamiltonian of the planetary problem into the poisson series in all Keplerian elements (theory) (2001) Astron. Vestn., 35 (3), pp. 267-272; (2001) Sol. Syst. Res. (Engl. Transl., 35 (3), pp. 243-248; Kholshevnikov, K.V., Greb, A.V., Kuznetsov, E.D., The expansion of the Hamiltonian of the two-planetary problem into a poisson series in all elements: Estimation and direct calculation of coefficients (2002) Astron. Vestn., 36 (1), pp. 75-87; (2002) Sol. Syst. Res. (Engl. Transl.), 36 (1), pp. 68-79; Moisson, X., Solar system planetary motion to third order of masses (1999) Astron. Astrophys., 341, pp. 318-327; Petrovskaya, M.S., Ivanova, T.V., Construction of expansions of the planetary perturbation function (1978) Byull. Inst. Teor. Astron., Akad. Nauk SSSR, 14 (5-158), pp. 288-293; Simon, J.L., Bretagnon, P., Chapront, J., Numerical expressions for precession formulae and mean elements for the moon and the planets (1994) Astron. Astrophys., 282, pp. 663-683; Subbotin, M.F., (1968) Vvedenie v Teoreticheskuyu Astronomiyu (An Introduction into Theoretical Astronomy), , Moscow: Nauka
Correspondence Address	Kuznetsov, E.D.; Ural State University, pr. Lenina 51, Yekaterinburg, 620083, Russian Federation
Language of Original Document	English
Abbreviated Source Title	Sol. Syst. Res.
Source	Scopus