Balancing with reflex delay

G. Stépán, L. Kollár

Research output: Contribution to journalArticle

46 Citations (Scopus)

Abstract

We consider the simplest possible model describing the 'man-machine' system when somebody places the end of a stick on his fingertip, and tries to move the lowest point of the stick in a way that its upper position should be stable. The stability analysis of the mechanical model provides surprisingly simple and clear results in spite of the fact that modelling the time delay makes the corresponding differential equation infinite dimensional in mathematical sense. The calculated critical delay of reflexes and the frequency of the nonlinear vibrations arising as a result of a Hopf bifurcation at the limit of linear stability shows good agreement with experimental observations. By means of the above results, we also get some in-view into the work of the organ called 'labyrinthus' in the inner ear which helps in self-balancing of the human body even when our eyes are closed. (C) 2000 Elsevier Science Ltd.

Original languageEnglish
Pages (from-to)199-205
Number of pages7
JournalMathematical and Computer Modelling
Volume31
Issue number4-5
DOIs
Publication statusPublished - Feb 2000

Fingerprint

Balancing
Man machine systems
Hopf bifurcation
Man-machine Systems
Time delay
Differential equations
Nonlinear Vibration
Linear Stability
Hopf Bifurcation
Stability Analysis
Time Delay
Lowest
Differential equation
Closed
Modeling
Model
Vibration
Stability analysis
Human body
Human

Keywords

  • Balancing
  • Delay
  • Hopf bifurcation
  • Inner ear

ASJC Scopus subject areas

  • Information Systems and Management
  • Control and Systems Engineering
  • Applied Mathematics
  • Computational Mathematics
  • Modelling and Simulation

Cite this

Balancing with reflex delay. / Stépán, G.; Kollár, L.

In: Mathematical and Computer Modelling, Vol. 31, No. 4-5, 02.2000, p. 199-205.

Research output: Contribution to journalArticle

Stépán, G. ; Kollár, L. / Balancing with reflex delay. In: Mathematical and Computer Modelling. 2000 ; Vol. 31, No. 4-5. pp. 199-205.
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