×

zbMATH — the first resource for mathematics

The use of CAS Piranha for the construction of motion equations of the planetary system problem. (English) Zbl 1383.70012
Kotsireas, Ilias S. (ed.) et al., Applications of computer algebra, Kalamata, Greece, July 20–23, 2015. Cham: Springer (ISBN 978-3-319-56930-7/hbk; 978-3-319-56932-1/ebook). Springer Proceedings in Mathematics & Statistics 198, 385-396 (2017).
Summary: In this paper, we consider the using of the computer algebra system Piranha as applied to the study of the planetary problem. Piranha is an echeloned Poisson series processor, which is written in C++ language. It is new, specified, high-efficient program for analytical transformations of polynomials, Fourier and Poisson series. We used Piranha for the expansion of the Hamiltonian of four-planetary problem into the Poisson series and the construction of motion equations by the Hori-Deprit method. Both of these algorithms are briefly presented in this work. Different properties of the series representation of the Hamiltonian and motion equations are discussed.
For the entire collection see [Zbl 1379.13001].
MSC:
70F15 Celestial mechanics
70-08 Computational methods for problems pertaining to mechanics of particles and systems
Software:
Piranha
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] 1. Poincare, H.: Les Methodes nouvelles de la Mecanique Celeste. Grauthier-Viltars, Paris (1892)
[2] 2. Murray, C.D., Dermott, S.F.: Solar System Dynamics. Cambridge University Press, Cambridge (1999) · Zbl 0957.70002
[3] 3. Charlier, C.L.: Die Mechanik des Himmels. Walter de Gruyter & Co., Berlin (1927) · JFM 53.0892.01
[4] 4. Kholshevnikov, K.V.: Asimptoticheskie metody nebesnoi mekhaniki. Asymptotic Methods in Celestial Mechanics. Leningr. Gos. Univ., Leningrad (1985)
[5] 5. Kuznetsov, E.D., Kholshevnikov, K.V.: Dynamical evolution of weakly disturbed two-planetary system on cosmogonic time scales: the Sun-Jupiter-Saturn system. Solar Syst. Res. 40 (3), 239-250 (2006)
[6] 6. Biscani, F.: The Piranha computer algebra system.
[7] 7. 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. Solar Syst. Res. 49 (6)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.