Astronomy and Astrophysics – Astronomy
Scientific paper
Jun 2009
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2009cemda.104..129t&link_type=abstract
Celestial Mechanics and Dynamical Astronomy, Volume 104, Issue 1-2, pp. 129-144
Astronomy and Astrophysics
Astronomy
Hamiltonian Dynamics, Averaging, Lie Series Method, Asteroid Dynamics
Scientific paper
A new mathematically correct approach to construct an averaging procedure for the motion of a massless body around the central body perturbed by fully interacting planets is developed and the errors of the standard solution are discussed. The new technique allows to combine the advantages of the Hamiltonian representation with the usage of standard osculating elements in combination with all the standard expansions of the perturbing functions. The main idea is to introduce new additional variables conjugate to all the standard elements and to work in a corresponding super phase space. In this way, the number of variables is doubled at first, but one has to deal with only one Hamiltonian. The artificially introduced variables disappear from the final averaged equations as well as from the transformation formulae connecting the osculating and the mean elements.
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