The Hori–Deprit method for averaged motion equations of the planetary problem in elements of the second Poincaré system / Perminov A.S., Kuznetsov E.D. // Solar System Research. - 2016. - V. 50, l. 6. - P. 426-436.

ISSN:
00380946
Type:
Article
Abstract:
We consider an algorithm to construct averaged motion equations for four-planetary systems by means of the Hori–Deprit method. We obtain the generating function of the transformation, change-variable functions and right-hand sides of the equations of motion in elements of the second Poincaré system. Analytical computations are implemented by means of the Piranha echeloned Poisson processor. The obtained equations are to be used to investigate the orbital evolution of giant planets of the Solar system and various extrasolar planetary systems. © 2016, Pleiades Publishing, Inc.
Author keywords:
equations of motion; Hori–Deprit method; planetary problem; Poisson brackets; Poisson processor; second system of Poincaré elements
Index keywords:
нет данных
DOI:
10.1134/S0038094616060022
Смотреть в Scopus:
https://www.scopus.com/inward/record.uri?eid=2-s2.0-85010064662&doi=10.1134%2fS0038094616060022&partnerID=40&md5=74a8d7b660cd0d59d71339ad6af318d7
Соавторы в МНС:
Другие поля
Поле Значение
Link https://www.scopus.com/inward/record.uri?eid=2-s2.0-85010064662&doi=10.1134%2fS0038094616060022&partnerID=40&md5=74a8d7b660cd0d59d71339ad6af318d7
Affiliations Ural Federal University, Yekaterinburg, Russian Federation
Author Keywords equations of motion; Hori–Deprit method; planetary problem; Poisson brackets; Poisson processor; second system of Poincaré elements
References Biscani, F., (2015) The Piranha computer algebra system, , https://github.com/bluescarni/piranha; Charlier, C.L., (1927) Die Mechanik de Himmels; Kholshevnikov, K.V., (1985) Asimptoticheskie metody nebesnoi mekhaniki (Asymptotic Methods for Celestial Mechanics), , Leningrad. Univ., Leningrad; Kuznetsov, E.D., Kholshevnikov, K.V., Dynamical evolution of weakly disturbed two-planetary system on cosmogonic time-scales: the Sun-Jupiter-Saturn system (2006) Solar Syst. Res., 40 (3), pp. 239-250; Perminov, A.S., Kuznetsov, E.D., Expansion of the Hamiltonian of the planetary problem into the Poisson series in elements of the second Poincare system (2015) Solar Syst. Res., 49 (6), pp. 430-441; Perminov, A.S., Kuznetsov, E.D., The way to generate the averaged equations of motion for planetary problem by means of Hori-Deprit method (2016) Izv. Glavnoi astronomicheskoi observatorii v Pulkove no. 223. Tr. Vserossiiskoi astrometricheskoi konferentsii “Pulkovo–2015, pp. 241-246. , Main Astronomical Observatory of the Russian Academy of Sciences at Pulkovo, St. Petersburg: Bulletin of the Main Astronomical Observatory of the Russian Academy of Sciences at Pulkovo no. 223. Proc. All-Russian Astronomic Conf. “Pulkovo–2015”; Perminov, A.S., Kuznetsov, E.D., Use computer algebra system piranha for expansion of the Hamiltonian and construction averaging motion equations of the planetary system problem (2016) Springer Proc. Math.; Subbotin, M.F., (1968) Vvedenie v teoreticheskuyu astronomiyu (Introduction into Theoretical Astronomy), , Nauka, Moscow
Correspondence Address Kuznetsov, E.D.; Ural Federal UniversityRussian Federation; email: eduard.kuznetsov@urfu.ru
Publisher Maik Nauka Publishing / Springer SBM
Language of Original Document English
Abbreviated Source Title Sol. Syst. Res.
Source Scopus