On Stability of the Inverted Pendulum Motion with a Vibrating Suspension Point

G. V. Demidenko, A. V. Dulepova

Research output: Contribution to journalArticlepeer-review

Abstract

Under study is the stability of the inverted pendulum motion whose suspension point vibrates according to a sinusoidal law along a straight line having a small angle with the vertical. Formulating and using the contracting mapping principle and the criterion of asymptotic stability in terms of solvability of a special boundary value problem for the Lyapunov differential equation, we prove that the pendulum performs stable periodic movements under sufficiently small amplitude of oscillations of the suspension point and sufficiently high frequency of oscillations.

Original languageEnglish
Pages (from-to)607-618
Number of pages12
JournalJournal of Applied and Industrial Mathematics
Volume12
Issue number4
DOIs
Publication statusPublished - 1 Oct 2018

Keywords

  • asymptotic stability
  • contracting mapping principle
  • inverted pendulum
  • Lyapunov differential equation

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