Astronomy and Astrophysics – Astronomy
Scientific paper
Jan 2006
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2006rmxac..25...32p&link_type=abstract
Third International Meeting of Dynamic Astronomy in Latin America (Eds. Carlos Abad, Ángel Bongiovanni, & Yaneth Guillén) Revist
Astronomy and Astrophysics
Astronomy
Celestial Mechanics, Planets And Satellites: General
Scientific paper
In the context of artificial satellite theory, we study the case of an artificial satellite around an Earth-like planet. The perturbation force taken into account is produced by the gravity attraction of the planet, and in particular, it is caused by its inhomogenous potential. Our analysis is purely analytical and we begin by truncating the Hamiltonian equations at second order, that is, considering the influence of the zonal and the tesseral harmonics to order two. The system is formulated as a Hamiltonian with three degrees of freedom. Then, by means of three successive Lie transforms, we normalise the system to order five in a small parameter. We do not use Taylor expansions of the eccentricity nor Fourier series in the anomalies. After these transformations are performed, the truncated and reduced Hamiltonian defines a system of one degree of freedom which can be written in terms of a collection of variables in a phase space which takes into account all of the symmetries of the problem. Next, an analysis of the system is performed, obtaining up to four relative equilibria and two types of bifurcations. The connection with the original system establishes the existence of various families of invariant tori, quasiperiodic and periodic trajectories with the same type of bifurcations as the reduced problem.
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