On the orbital stability of a periodic solution of the equations of motion of a Kovalevskaya gyroscope
type: Item
instance of: scholarly article
title: On the orbital stability of a periodic solution of the equations of motion of a Kovalevskaya gyroscope
zbMATH Open document ID: 0628.70021
DOI: 10.1016/0021-8928(86)90084-5
author: A. Z. Bryum
author: A. Ya. Savchenko
published in: Journal of Applied Mathematics and Mechanics
publication date: 1986-01-01T00:00:00Z
review text: The sufficient conditions for the orbital stability of a periodic solution of the equations of motion of a Kovalevskaya gyroscope in the case of Bobylev-Steklov integrability are obtained. It is difficult to expect Lyapunov stability for the unsteady motions of a heavy solid having a fixed point since a dependence of the vibrations frequency on the initial conditions is characteristic for the simplest of them, i.e. periodic motions. Moreover, a rougher property of periodic solutions of the Euler-Poisson equations, orbital stability, is not the subject of special investigations in the dynamics of a solid. The algorithm of the present investigation utilizes the treatment ascribed Zhukovskii of orbital stability as the Lyapunov stability of motion for a special selection of the variable playing the part of time and the Chetayev method of constructing Lyapunov functions from the first integrals of the equations of perturbed motion. This latter circumstance enables the Chetayev method to be put in one series with the methods used earlier.
Mathematics Subject Classification ID: 70K20
Mathematics Subject Classification ID: 70E20
Mathematics Subject Classification ID: 37D45
zbMATH DE Number: 4022697
zbMATH Keywords: sufficient conditions
zbMATH Keywords: orbital stability
zbMATH Keywords: periodic solution
zbMATH Keywords: Kovalevskaya gyroscope
zbMATH Keywords: Bobylev-Steklov integrability
zbMATH Keywords: initial conditions
zbMATH Keywords: Euler- Poisson equations
zbMATH Keywords: Lyapunov stability
zbMATH Keywords: Chetayev method
zbMATH Keywords: first integrals of the equations of perturbed motion
MaRDI profile type: Publication
full work available at URL: 0021-8928(86)90084-5
OpenAlex ID: W2088566535
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description: scientific article; zbMATH DE number 4022697