Abstract
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.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Poincare, H.: Les Methodes nouvelles de la Mecanique Celeste. Grauthier-Viltars, Paris (1892)
Murray, C.D., Dermott, S.F.: Solar System Dynamics. Cambridge University Press, Cambridge (1999)
Charlier, C.L.: Die Mechanik des Himmels. Walter de Gruyter & Co., Berlin (1927)
Kholshevnikov, K.V.: Asimptoticheskie metody nebesnoi mekhaniki. Asymptotic Methods in Celestial Mechanics. Leningr. Gos. Univ., Leningrad (1985)
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)
Biscani, F.: The Piranha computer algebra system. https://github.com/bluescarni/piranha (2015)
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), 430–441 (2015)
Acknowledgements
The authors are grateful to Francesco Biscani for the implementation of echeloned Poisson series in Piranha and his help with technical questions. This work is supported by Act 211 Government of the Russian Federation, agreement 02.A03.21.0006.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2017 Springer International Publishing AG
About this paper
Cite this paper
Perminov, A.S., Kuznetsov, E.D. (2017). The Use of CAS Piranha for the Construction of Motion Equations of the Planetary System Problem . In: Kotsireas, I., Martínez-Moro, E. (eds) Applications of Computer Algebra. ACA 2015. Springer Proceedings in Mathematics & Statistics, vol 198. Springer, Cham. https://doi.org/10.1007/978-3-319-56932-1_25
Download citation
DOI: https://doi.org/10.1007/978-3-319-56932-1_25
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-56930-7
Online ISBN: 978-3-319-56932-1
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)