Multiple Resonance in One Problem of the Stability of the Motion of a Satellite Relative to the Center of Mass

Details Multiple Resonance in One Problem of the Stability of the Motion of a Satellite Relative to the Center of Mass Multiple Resonance in One Problem of the Stability of the Motion of a Satellite Relative to the Center of Mass

Sep 2005

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2005astl...31..627m&link_type=abstract

Astronomy Letters, vol. 31, Issue 9, p.627-633

Astronomy and Astrophysics

Astronomy

Celestial Mechanics - Resonance - Stability - Periodic Motion - Satellite

Scientific paper

We investigate the stability of the periodic motion of a satellite, a rigid body, relative to the center of mass in a central Newtonian gravitational field in an elliptical orbit. The orbital eccentricity is assumed to be low. In a circular orbit, this periodic motion transforms into the well-known motion called hyperboloidal precession (the symmetry axis of the satellite occupies a fixed position in the plane perpendicular to the radius vector of the center of mass relative to the attractive center and describes a hyperboloidal surface in absolute space, with the satellite rotating around the symmetry axis at a constant angular velocity). We consider the case where the parameters of the problem are close to their values at which a multiple parametric resonance takes place (the frequencies of the small oscillations of the satellite’s symmetry axis are related by several second-order resonance relations). We have found the instability and stability regions in the first (linear) approximation at low eccentricities.

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