A method for the expansion of the perturbative Hamiltonian in the planetary problem is presented, which allows one to immediately detect the terms vanishing under the averaging process. The method bases itself on a geometrical analysis, through the groups SO(3) and SU(2), of the Poincaré canonical variables or of the similar Laplace variables. As an outcome, one obtains a MAPLE program, which calculates the first averaged terms of the perturbative Hamiltonian.
Geometry of Poincaré's variables and the secular planetary problem / Bruno Cordani. - In: CELESTIAL MECHANICS & DYNAMICAL ASTRONOMY. - ISSN 0923-2958. - 89:2(2004), pp. 165-179.
Geometry of Poincaré's variables and the secular planetary problem
Bruno Cordani
2004
Abstract
A method for the expansion of the perturbative Hamiltonian in the planetary problem is presented, which allows one to immediately detect the terms vanishing under the averaging process. The method bases itself on a geometrical analysis, through the groups SO(3) and SU(2), of the Poincaré canonical variables or of the similar Laplace variables. As an outcome, one obtains a MAPLE program, which calculates the first averaged terms of the perturbative Hamiltonian.
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