Stability of the planetary three-body problem

• DOI: 10.1007/bf00692088
• Publication Date: 2004-11-29T09:25:18Z
• Authors: Jacques Laskar; Philippe Robutel
• Keywords: [SDU.ASTR]Sciences of the Universe [physics]/Astrophysics [astro-ph]; 0103 physical sciences; [SDU.ASTR] Sciences of the Universe [physics]/Astrophysics [astro-ph]; 01 natural sciences

We present a direct method for the expansion of the planetary Hamiltonian in Poincare 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.