Piranha

The use of CAS Piranha for the construction of motion equations of the planetary system problem. 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.

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