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. 6. - P. 430-441.

ISSN/EISSN:

0038-0946 / 1608-3423

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.

Author keywords:

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

DOI:

10.1134/S0038094615050081

Web of Science ID:

ISI:000388315700008

Соавторы в МНС:

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Другие поля

Поле	Значение
Month	NOV
Publisher	MAIK NAUKA/INTERPERIODICA/SPRINGER
Address	233 SPRING ST, NEW YORK, NY 10013-1578 USA
Language	English
EISSN	1608-3423
Research-Areas	Astronomy \& Astrophysics
Web-of-Science-Categories	Astronomy \& Astrophysics
Author-Email	perminov12@yandex.ru eduard.kuznetsov@urfu.ru
Funding-Acknowledgement	Government of the Russian Federation {[}02.A03.21.0006]
Funding-Text	The work was supported by Act 211 Government of the Russian Federation, contract 02.A03.21.0006.
Number-of-Cited-References	8
Usage-Count-Last-180-days	1
Usage-Count-Since-2013	2
Journal-ISO	Solar Syst. Res.
Doc-Delivery-Number	EC7KC