Gimbal suspension gyro: Stability, bifurcation, and chaos
type: Item
instance of: scholarly article
title: Gimbal suspension gyro: Stability, bifurcation, and chaos
zbMATH Open document ID: 1065.70005
DOI: 10.1023/A:1013095729256
author: S. A. Agafonov
published in: Journal of Dynamical and Control Systems
publication date: 2003-04-27T00:00:00Z
review text: The paper deals with mechanical model of gimballed gyroscope -- balanced gimbal suspension gyro (GSG) which is installed on an immovable base. External gimbal ring is under the action of viscous friction moment and moment represented by some function of the angle between external ring plane and normal vector to internal ring plane, in steady motion these planes are orthogonal. Firstly, a stability condition of uniform rotation of GSG is carried out and analyzed by means of Lyapunov's function. Also an estimation of the attraction set is obtained. Secondly, the mechanism of stability loss, when the bifurcational parameter achieves the critical value, is described. In this case a periodic motion appears, and a condition of its orbital stability is found. The third part of the paper is the investigation of forced vibration of GSG. For unperturbed system the equation of separatrix which passes through the hyperbolic points is found. To determine the condition of intersection of separatrices for perturbed system, Melnikov's distance is calculated. Its value characterises the arising of chaotic motion in the space of system's parameters.
reviewed by: Vladimir Evgenievich Puzyrev
Mathematics Subject Classification ID: 70E05
Mathematics Subject Classification ID: 70K50
Mathematics Subject Classification ID: 70K55
Mathematics Subject Classification ID: 37N05
zbMATH DE Number: 1901435
zbMATH Keywords: Lyapunov function
zbMATH Keywords: forced vibration
zbMATH Keywords: Melnikov distance
MaRDI profile type: Publication
full work available at URL: a:1013095729256
OpenAlex ID: W2044411624
description: scientific article; zbMATH DE number 1901435