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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References
Abdullah K. and Albouy A.: 2001, 'On a strange resonance noticed by M. Herman'. Regul. Chaotic Dyn., 6, 421–432.
Brower D. and Clemence G.M.: 1961, Methods of Celestial Mechanics. Academic Press, New York, London.
Cordani B.: 2003, The Kepler Problem. Group Theoretical Aspect, Regularization and Quantization, with an Application to the Study of Perturbations. Birkhäuser, Basel.
Laskar J. and Robutel P.: 1995, 'Stability on the planetary three–body problem. I–Expansion of the planetary Hamiltonian'. Celestial Mechanics and Dynamical Astronomy, 62, 193–217.
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Cordani, B. Geometry of Poincaré's Variables and the Secular Planetary Problem. Celestial Mechanics and Dynamical Astronomy 89, 165–179 (2004). https://doi.org/10.1023/B:CELE.0000034512.34892.b1
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DOI: https://doi.org/10.1023/B:CELE.0000034512.34892.b1