Resonance in Satellite's Motion Under Air Drag

This article studies the attitude motion of a satellite in a circular orbit under the influence of central body of mass M and its moon of mass m, whose orbit is assumed to be circular and coplanar with the orbit of the satellite. The body is assumed to be tri-axial body with principal moments of inertia A < B < C at its centre of mass, C is the moment of inertia about the spin axis which is perpendicular to the orbital plane. These principal axes are taken as the co-ordinate axes x, y, z; the z axis being perpendicular to the orbital plane. We have studied the rotational motion of satellite in the circular orbit under the influence of aerodynamic torque. Using BKM method, it is observed that the amplitude of the oscillation remains constant upto the second order of approximation. The main and the parametric resonance have been shown to exist and have been studied by BKM method. The analysis regarding the stability of the stationary planar oscillation of a satellite near the resonance frequency shows that the discontinuity occurs in the amplitude of the oscillation at a frequency of the external periodic force which is less than the frequency of the natural oscillation.