Stability of the synchronous spin-orbit resonance by construction of librational trapping tori

Details Stability of the synchronous spin-orbit resonance by construction of librational trapping tori Stability of the synchronous spin-orbit resonance by construction of librational trapping tori

Oct 1993

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1993cemda..57..325c&link_type=abstract

Celestial Mechanics and Dynamical Astronomy (ISSN 0923-2958), vol. 57, no. 1-2, p. 325-328

Astronomy and Astrophysics

Astronomy

1

Astronomical Models, Libration, Orbit Calculation, Orbital Resonances (Celestial Mechanics), Planetary Orbits, Satellite Perturbation, Solar System, Spin Stabilization, Hamiltonian Functions, Mathematical Models, Satellite Rotation, Toruses

Scientific paper

The stability of the 1:1 resonance is studied by applying perturbation techniques. This paper is a short presentation of the method developed by Celletti (1993). Let S be a triaxial ellipsoidal satellite rotating about an internal spin-axis and at the same time revolving around a central body P. A spin-orbit resonance means an exact commensurability between the periods of rotation and revolution of the satellite. In particular, a 1:1 (or synchronous resonance) implies that the period of rotation and the period of resolution are identically equal. The physical model is reduced by making some simplified assumptions which are generally satisfied by most satellites of the solar system. A method for constructing the librational surfaces is shown. To this end, a suitable Hamiltonian function is computed, performing some area-preserving changes of variables. In order to construct librational tori, the KAM theorem is applied using the algorithm developed in Celletti and Chierchia (1987).

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