Expansion of the Hamiltonian of the planetary problem into the Poisson series in elements of the second Poincare system / Perminov A.S., Kuznetsov E.D. // Solar System Research. - 2015. - V. 49, l. 7. - P. 430-441.

ISSN:

00380946

Type:

Article

Abstract:

The Hamiltonian of the N-planetary problem is written in the Jacobi coordinates using the second system of Poincare elements. The Hamiltonian is expanded into the Poisson series for the four-planet system. The computer algebra system Piranha is used for analytical transformations. Obtained expansions provide the Hamiltonian expression accuracy up to the third degree of the small parameter for giant planets of the Solar System and up to the second degree of the small parameter for extrasolar planetary systems. The ratio of sums of masses of the planets to the star mass can be selected as a small parameter. © 2015, Pleiades Publishing, Inc.

Author keywords:

and Poisson processor; Hamiltonian; Jacobi coordinate system; N-planetary problem; Poisson series; second system of Poincare elements

Index keywords:

нет данных

DOI:

10.1134/S0038094615050081

Смотреть в Scopus:

https://www.scopus.com/inward/record.uri?eid=2-s2.0-84947079085&doi=10.1134%2fS0038094615050081&partnerID=40&md5=0f44ec25de2e3522c2f9bfd3f1c07335

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Поле	Значение
Link	https://www.scopus.com/inward/record.uri?eid=2-s2.0-84947079085&doi=10.1134%2fS0038094615050081&partnerID=40&md5=0f44ec25de2e3522c2f9bfd3f1c07335
Affiliations	Ural Federal University, Yekaterinburg, Russian Federation
Author Keywords	and Poisson processor; Hamiltonian; Jacobi coordinate system; N-planetary problem; Poisson series; second system of Poincare elements
References	Biscani, F., (2009) The Piranha algebraic manipulator; Charlier, C.L., (1927) Die Mechanik des Himmels, , Walter de Gruyter & Co, Berlin, Leipzig; Folkner, W.M., Williams, J.G., Boggs, D.H., JPL planetary and lunar ephemeris DE421 (2008) Interoffice Memorandum; 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) Solar Syst. Res., 35 (3), pp. 243-248; Kholshevnikov, K.V., Kuznetsov, E.D., Review of the works on the orbital evolution of solar system major planets (2007) Solar Syst. Res., 41 (4), pp. 265-300; Murray, C.D., Dermott, S.F., (1999) Solar System Dynamics, , Cambridge Univ. Press, Cambridge; Schneider, J., (2010) The Extrasolar Planets Encyclopedia, , http://exoplaneteu Subbotin; Subbotin, M.F., (1968) Vvedenie v teoreticheskuyu astronomiyu (Introduction into Theoretical Astronomy), , Moscow, Nauka
Correspondence Address	Perminov, A.S.; Ural Federal UniversityRussian Federation
Publisher	Maik Nauka Publishing / Springer SBM
Language of Original Document	English
Abbreviated Source Title	Sol. Syst. Res.
Source	Scopus