Fractional analysis of induced resonance effects in the spherical motion of a rigid body with flywheels

The evolution of the motion of an asymmetric rigid body with flywheels can be explored by the methods of asymptotic analysis. It is shown, that the effect of small moments resulting from the displacement of the center of mass and of small control moments from the flywheels lead to the emergence of non-linear resonance evolutionary effects. The aim of this work is to investigate the resonance effects and analyze their influence on the change of the fast phase in the spherical motion of the asymmetrical rigid body with flywheels. To explore these resonance effects we applied the method of integral manifolds and the averaging method. The averaged equations showed that resonance effects can lead to the regular precession, to the formation of stationary points, or to the prolonged resonance. In addition, the characteristic features of the influence of secondary resonance effects on the change in the fast phase are revealed. (paper)