Stability of the Planetary Three-Body Problem. I. Expansion of the Planetary Hamiltonian

Astronomy and Astrophysics – Astronomy

Scientific paper

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Planetary Motion, Perturbation Function, Celestial Mechanics, Computer Algebra

Scientific paper

We present a direct method for the expansion of the planetary Hamiltonian in Poincaré canonical elliptic variables with its effective implementation in computer algebra. This method allows us to demonstrate the existence of simplifications occurring in the analytical expression of the Hamiltonian coefficients. All the coefficients depending on the ratio of the semi major axis can thus be expressed in a concise and canonical form.

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