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Stability and Longitudinal Resonances of the Kapitsa Pendulum
Nikita F. Morozov, Oksana R. Polyakova, Tatyana P. Tovstik
1 - 6
10.3233/FAIA231169
Research Article
Frontiers in Artificial Intelligence and Applications
Volume 381: Electronics, Communications and Networks
Abstract

The generalized Kapitsa problem of stabilizing the upper position of a deformable pendulum under the action of small vertical oscillations of its base in a gravity field is solved. The presence of a small parameter of the problem allows us to carry out averaging and obtain approximate equations of motion of the pendulum. Two models of a pendulum are considered and compared: a flexible inextensible rod and a flexible tensile rod. The influence of each parameter of the problem on stability is studied. The limits of applicability of the model of a flexible inextensible pendulum are obtained.

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