The stability of the vertical position of an inverted pendulum under the action of support vibration and the attraction basin of this position are considered. In addition to the classical Kapitsa problem for the harmonic vibration of a support, the polyharmonic and random vibration of the support are investigated. The condition of stability of the vertical position is determined, and the attraction basin of this stable position is investigated.
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Translated by V. Bukhanov
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Morozov, N.F., Belyaev, A.K., Tovstik, P.E. et al. Attraction Basins in the Generalized Kapitsa Problem. Dokl. Phys. 64, 335–339 (2019). https://doi.org/10.1134/S1028335819080056