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Acta Mechanica
Published in: Acta Mechanica 9/2021

21-06-2021 | Original Paper

On the instability of equilibria of mechanical systems in nonpotential force fields in the case of typical degeneracies

Author: Valery V. Kozlov

Published in: Acta Mechanica | Issue 9/2021

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Abstract

This paper addresses the problem of stability of equilibria of mechanical systems in nonpotential force fields. In the linear approximation, any nonpotential force is uniquely represented as the sum of a potential force and a circulatory force. The instability of equilibrium is established for the nonlinear problem in the case when the linearized system has a pair of zero eigenvalues. The mechanism of stability loss is due to the appearance of two asymptotic trajectories, one that enters an equilibrium point and one that exits it. A similar result takes place when additional gyroscopic forces and viscous friction forces are taken into account. Asymptotic solutions can be obtained in the form of series in inverse powers of time whose coefficients are polynomials in logarithms of time.
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Metadata
Title
On the instability of equilibria of mechanical systems in nonpotential force fields in the case of typical degeneracies
Author
Valery V. Kozlov
Publication date
21-06-2021
Publisher
Springer Vienna
Published in
Acta Mechanica / Issue 9/2021
Print ISSN: 0001-5970
Electronic ISSN: 1619-6937
DOI
https://doi.org/10.1007/s00707-021-03012-6

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