The inverse problem of stabilization of a spherical pendulum in a given position under oblique vibration.
DOI:
https://doi.org/10.21638/spbu01.2021.206Abstract
The inverse problem is posed of stabilizing a spherical pendulum (a mass point at the end of a weightless solid rod of length l ) in a given position using high-frequency vibration of the suspension point. The position of the pendulum is determined by the angle between the pendulum rod and the gravity acceleration vector. For any given position of the pendulum, a series of oblique vibration parameters (amplitude of the vibration velocity and the angle between the vibration velocity vector and the vertical) were found that stabilize the pendulum in this position. From the obtained series of solutions, the parameters of optimal vibration (vibration with a minimum amplitude of velocity) are selected depending on the position of the pendulum. The region of initial conditions is studied, of which the optimal vibration leads the pendulum to a predetermined stable position after a sufficiently long time. This area, following N. F.Morozov et al., called the area of attraction.Keywords:
spherical pendulum, stability, vibration of the suspension point, inverse problem
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References
Литература
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Published
2021-07-21
How to Cite
Petrov А. G. (2021). The inverse problem of stabilization of a spherical pendulum in a given position under oblique vibration. Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 8(2), 255–269. https://doi.org/10.21638/spbu01.2021.206
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Section
In memoriam of P. E. Tovstik
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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.
