On stabilizability of the upper equilibrium of the asymmetrically excited inverted pendulum

Csizmadia, László: On stabilizability of the upper equilibrium of the asymmetrically excited inverted pendulum. Electronic journal of qualitative theory of differential equations 45. pp. 1-19. (2018)

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Abstract

Using purely elementary methods, necessary and sufficient conditions are given for the existence of T-periodic and 2T-periodic solutions around the upper equilibrium of the mathematical pendulum when the suspension point is vibrating vertically with asymmetric high frequency. The equation of the motion is of the form 1 l (g + a(t)) θ = 0, where a(t) := Ah , if kT ≤ t < kT + Th −Ae , if kT + Th ≤ t < (kT + Th ) + Te (k = 0, 1, . . .); Ah , Ae , Th , Te are positive constants (Th + Te = T); g and l denote the acceleration of gravity and the length of the pendulum, respectively. An extended Oscillation Theorem is given. The exact stability regions for the upper equilibrium are presented.

Item Type: Article
Journal or Publication Title: Electronic journal of qualitative theory of differential equations
Date: 2018
Number: 45
Page Range: pp. 1-19
ISSN: 1417-3875
DOI: https://doi.org/10.14232/ejqtde.2018.1.45
Uncontrolled Keywords: Differenciálegyenlet
Additional Information: Bibliogr.: p. 17-19. ; összefoglalás angol nyelven
Date Deposited: 2019. Jun. 03. 06:10
Last Modified: 2019. Jun. 03. 06:10
URI: http://acta.bibl.u-szeged.hu/id/eprint/58140

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