The results of investigation of a new phenomenon represented by the revolving of stiff rotor in elastic supports with four self-balanced pendulums are discussed in the article. The rotor is rotating with some operating velocity but the pendulums are moving with a frequency which equals one from two critical velocities of the rotor rotation connected with its linear or angular motion parameters. The procedure of mathematical models construction for system with eight degrees of freedom is offered. Dynamical interactions’ properties between partial systems with definite forms of a motion self-organization in a freely suspended pendulum group are discussed.

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The article describes the results of an experimental study of the natural frequencies of oscillations of a mechanical system influence on the angular velocity of a pendulum mounted with the possibility of free rotation on a rotating shaft of an electric motor. It is established that at a constant moment of friction in the pendulum support, providing for a change in its mass moment of inertia, a mode of motion takes place in which the motor shaft rotates at a working angular velocity, and the angular velocity of the pendulum coincides with one of the natural frequencies of the oscillations of the mechanical system. The studies have also shown that there are ranges of the values of moments of inertia of the pendulum mass. For these moments of inertia, one can observe the establishment of a stable or unstable angular velocity of the pendulum, which is equal to one of the natural frequencies of the oscillations of the mechanical system.

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Using the methods of the small parameter of nonlinear mechanics, the formulas for determining the parameters of the pendulum auto-balancer were obtained in the article. Conditions for the stability of the auto-balancing process of the unbalanced rotor, fastened in the housing on the elastic supports, were also found. It is established that the stable operation of the auto-balancer can be implemented in the angular velocity ranges of the rotor due to the choice of the stiffness characteristics of the elastic supports.