Geodesic
On periodic solutions of one second-order differential equation
Contemporary Mathematics. Fundamental Directions, Dedicated to 70th anniversary of the President of the RUDN University V. M. Filippov, Tome 67 (2021) no. 3, pp. 535-548

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In this paper, we investigate the movement of an inverted pendulum, the suspension point of which performs high-frequency oscillations along a line making a small angle with the vertical. We prove that under certain conditions on the function describing the oscillations of the suspension point of the pendulum, a periodic motion of the pendulum arises, and it is asymptotically stable. 
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     author = {G. V. Demidenko and A. V. Dulepova},
     title = {On periodic solutions of one second-order differential equation},
     journal = {Contemporary Mathematics. Fundamental Directions},
     pages = {535--548},
     publisher = {mathdoc},
     volume = {67},
     number = {3},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/CMFD_2021_67_3_a8/}
}
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G. V. Demidenko; A. V. Dulepova. On periodic solutions of one second-order differential equation. Contemporary Mathematics. Fundamental Directions, Dedicated to 70th anniversary of the President of the RUDN University V. M. Filippov, Tome 67 (2021) no. 3, pp. 535-548. http://geodesic.mathdoc.fr/item/CMFD_2021_67_3_a8/