Resonant and non-resonant gravity-gradient perturbations of a tumbling tri-axial satellite.

Details Resonant and non-resonant gravity-gradient perturbations of a tumbling tri-axial satellite. Resonant and non-resonant gravity-gradient perturbations of a tumbling tri-axial satellite.

Sep 1971

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1971cemec...3..346h&link_type=abstract

Celestial Mechanics, Volume 3, Issue 3, pp.346-383

Physics

13

Scientific paper

Gravity-gradient perturbations of the attitude motion of a tumbling tri-axial satellite are investigated. The satellite center of mass is considered to be in an elliptical orbit about a spherical planet and to be tumbling at a frequency much greater than orbital rate. In determining the unperturbed (free) motion of the satellite, a canonical form for the solution of the torque-free motion of a rigid body is obtained. By casting the gravity-gradient perturbing torque in terms of a perturbing Hamiltonian, the long-term changes in the rotational motion are derived. In particular, far from resonance, there are no long-period changes in the magnitude of the rotational angular momentum and rotational energy, and the rotational angular momentum vector precesses abound the orbital angular momentum vector. At resonance, a low-order commensurability exists between the polhode frequency and tumbling frequency. Near resonance, there may be small long-period fluctuations in the rotational energy and angular momentum magnitude. Moreover, the precession of the rotational angular momentum vector about the orbital angular momentum vector now contains substantial long-period contributions superimposed on the non-resonant precession rate. By averaging certain long-period elliptic functions, the mean value near resonance for the precession of the rotational angular momentum vector is obtained in terms of initial conditions.

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