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A. Belyakov:
"Another mechanical model of parametrically excited pendulum and stabilization of its inverted equilibrium position";
in: "Proceedings of the 8th European Nonlinear Dynamics Conference (ENOC 2014)", herausgegeben von: Institute of Mechanics and Mechatronics, Vienna University of Technology; Institute of Mechanics and Mechatronics, Vienna University of Technology, 2014, ISBN: 978-3-200-03433-4.

A new mechanical model of parametrically excited pendulum is proposed. The pendulum consists of two identical masses vibrating symmetrically along a circle. The model is mathematically equivalent to the pendulum with vertically vibrating pivot. Hence, the same parametric resonances and dynamic regimes can be observed. But the new mechanical realization provides different explanations of e.g. such phenomenon as high frequency stabilization of the inverse vertical position. Effect of damping on stabilization of the inverse vertical position is studied. It is observed that increase of damping can shift the stability domain of the inverse vertical position, i.e. damping can both stabilize and destabilize this equilibrium position. Similarity between the stability domains for harmonic and piecewise-constant periodic excitation functions for small parameters is demonstrated.