Stability of permanent rotations of interconnected rigid bodies system with small asymmetry

The influence of small asymmetry on stability of permanent rotations of interconnected rigid bodies is investigated. The velocities in the neighborhoods of those where the motion of system with small asymmetry is unstable are defined. Those critical velocities are named the resonance ones. It is established that if the rotation velocities of the system coincide with those of resonance then the characteristic equation of a symmetrical system has multiple roots. The algorithm of defining of the resonance velocities for a mechanical system of connected rigid bodies is designed. The resonance velocities of a system of n rigid bodies connected by elastic universal joints have been defined. The introduced discrete system is used for investigation of small oscillations of elastic rotating rods.