N-parametric canonical perturbation method based on Lie transforms. Application to the analysis of perturbations on multiple stellar systems

Details N-parametric canonical perturbation method based on Lie transforms. Application to the analysis of perturbations on multiple stellar systems N-parametric canonical perturbation method based on Lie transforms. Application to the analysis of perturbations on multiple stellar systems

Oct 2010

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2010aipc.1283..114a&link_type=abstract

MATHEMATICS AND ASTRONOMY: A JOINT LONG JOURNEY: Proceedings of the International Conference. AIP Conference Proceedings, Volum

Astronomy and Astrophysics

Astronomy

Binary Stars, Celestial Mechanics, Lie Algebras, Satellites, Artificial, Astrometric And Interferometric Binaries, Celestial Mechanics, Lie Algebras Of Lie Groups, Artificial Earth Satellites

Scientific paper

Recently, in order to analytically solve perturbation problems involving an arbitrary number of small parameters in the Hamiltonian formulation, a multiparametric theory based on Lie transforms theory was derived by the author [5]. It is a complete generalization of the Hori-Deprit method for N parameters with N arbitrary.
This method has been used to solve the classical Gyldén-Meščerskij problem-the relative motion of a binary system the components of which are losing mass over time-when the primary's oblateness, as well as relativistic effects, are taken into account. In addition, speed and accuracy comparisons between this analytical method and a numerical one (implicit Runge-Kutta) were also performed.

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