Areas of attraction of the pendulum under the influence of oblique vibration of the suspension point
DOI:
https://doi.org/10.21638/spbu01.2021.312Abstract
The inverse problem of stabilizing a spherical pendulum in a given position by means of high-frequency vibration of the suspension point is posed. The position of the pendulum is determined by the angle between the pendulum rod and the vertical. For any given position of the pendulum, a one-parameter series of oblique vibration characteristics (the amplitude of the vibration velocity and the angle between the vibration velocity vector and the vertical) is found to stabilize the pendulum in this position. For the obtained series, the regions of attraction are determined (the initial points from which a given stable position of the pendulum will be established under the influence of vibration).Keywords:
spherical pendulum, stability, vibration of the suspension point, inverse problem, region of attraction
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Литература
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Published
2021-09-26
How to Cite
Petrov А. G. (2021). Areas of attraction of the pendulum under the influence of oblique vibration of the suspension point. Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 8(3), 511–522. https://doi.org/10.21638/spbu01.2021.312
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Mechanics
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Articles of "Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy" are open access distributed under the terms of the License Agreement with Saint Petersburg State University, which permits to the authors unrestricted distribution and self-archiving free of charge.
