External stability of resonances in the motion of an asymmetric rigid body with a strong magnet in the geomagnetic field

We consider a precession motion, close to the classical Lagrange case, of an asymmetric rigid body with a strong magnet in an orbit in the geomagnetic field. For the principal moment we take the restoring torque due to the interaction between the planet magnetic fields and the rigid body. The perturbing actions are due to small moments of the rigid body mass-inertial asymmetry and small constant moments. We show that these perturbations result in the realization of secondary resonance effects in the rotational motion of the rigid body caused by the influence of resonance denominators in higher-order approximations of the averaging method. These effects were discovered in the study of rotational motion of a satellite with a magnetic damper in the nearly Euler case. In the present paper, we analyze both the secondary resonance effects themselves and the external stability of resonances. We obtain conditions ensuring a decrease in the angular velocity of the rigid body rotation about its center of mass. We also discover several new laws of influence of resonances on the nonresonance evolution of slow variables, which is related to the appearance of stable resonances.