Stability of Permanent Rotations of Interconnected Rigid Bodies System with Small Asymmetry

The influence of small asymmetry on stability of permanentrotations of interconnected rigid bodies is investigated. The velocitiesin the neighborhoods of those where the motion of system with smallasymmetry is unstable are defined. Those critical velocities are namedthe resonance ones. It is established that if the rotation velocities ofthe system coincide with those of resonance then the characteristicequation of a symmetrical system has multiple roots. The algorithm ofdefining of the resonance velocities for a mechanical system ofconnected rigid bodies is designed. The resonance velocities of a systemof n rigid bodies connected by elastic universal jointshave been defined. The introduced discrete system is used forinvestigation of small oscillations of elastic rotating rods.