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On the instability of equilibria of conservative systems under typical degenerations

On the instability of equilibria of conservative systems under typical degenerations We study systems of differential equations admitting first integrals with degenerate critical points. We find conditions for the instability of equilibria for the cases in which the first integral loses the minimum property. Results of general nature are used in the proof of the impossibility of gyroscopic stabilization of equilibria in conservative mechanical systems under simple typical bifurcations. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Differential Equations Springer Journals

On the instability of equilibria of conservative systems under typical degenerations

Kozlov, V.
Differential Equations , Volume 44 (8) – Oct 18, 2008
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References (2)

Publisher
Springer Journals
Copyright
Copyright © 2008 by MAIK Nauka
Subject
Mathematics; Difference and Functional Equations; Partial Differential Equations; Ordinary Differential Equations
ISSN
0012-2661
eISSN
1608-3083
DOI
10.1134/S001226610808003X
Publisher site
See Article on Publisher Site

Abstract

We study systems of differential equations admitting first integrals with degenerate critical points. We find conditions for the instability of equilibria for the cases in which the first integral loses the minimum property. Results of general nature are used in the proof of the impossibility of gyroscopic stabilization of equilibria in conservative mechanical systems under simple typical bifurcations.

Journal

Differential Equations – Springer Journals

Published: Oct 18, 2008

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