Journal ArticleDOI
On Lyapunov stability of dissipative mechanical systems
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TLDR
In this article, a sufficient condition for linear stability of dissipative mechanical systems with circulatory forces is derived, which has important applications in plasma physics, and it is shown that dissipative systems which are more than marginally stable without gyroscopic and circulatory force, remain stable after the addition of weak but finite gyroscopy and circulation forces.About:
This article is published in Physics Letters A.The article was published on 1999-07-05. It has received 10 citations till now. The article focuses on the topics: Dissipative system & Lyapunov stability.read more
Citations
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Gyroscopic stabilization of non-conservative systems
TL;DR: In this article, the stability of a linear conservative system can be improved or destroyed by weak damping and circulatory forces, governed by the Whitney umbrella singularity of the boundary of the asymptotic stability domain of the perturbed system.
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Lyapunov stability of abstract nonlinear dynamic system in Banach space
Genqi Xu,Siu Pang Yung +1 more
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A sufficient condition for instability of equilibrium of non-conservative undamped systems
TL;DR: In this article, a sufficient condition for instability of equilibrium of non-conservative undamped mechanical systems is established, which does not require spectral (eigenvalue) calculation and can be expressed as follows:
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On Lyapunov stability of nonautonomous mechanical systems
TL;DR: In this paper, a sufficient condition for the linear stability of non-autonomous dissipative mechanical systems with circulatory forces is derived and applied to autonomous systems transformed to nonautonomous ones by a time-dependent orthogonal transformation.
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Wall stabilization and the Mathieu–Hill equations
TL;DR: Tasso and Throumoulopoulos as discussed by the authors showed that parametric excitations can be stabilized by dissipation for positive potential energies, which broadens the regions of stability to the extent that not only the response to parametric exurations is damped, but even negative energy modes are stabilized by the combined action of the parametric and the damping coefficient.
References
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Journal ArticleDOI
Energy principle for dissipative two-fluid plasmas
TL;DR: In this paper, an energy principle for the dissipative two-fluid theory in Lagrangian form is given, which represents a necessary and sufficient condition for stability allowing the use of test functions.
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On the stability of dissipative mechanical systems with circulatory forces
TL;DR: In this article, the stability of a nonlinear dissipative mechanical system subjected to potential forces, gyroscopic forces, Rayleigh damping and circulatory forces was investigated using the direct Liapunov method.
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Linear and Nonlinear Stability in Resistive Magnetohydrodynamics.
TL;DR: In this paper, a sufficient stability condition with respect to purely growing modes is derived for resistive magnetohydrodynamics, and its "nearness" to necessity is analysed. But it is not shown that the condition is sufficient for all modes.
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A manifest Hopf bifurcation in resistive magnetohydrodynamics
TL;DR: A special Hopf bifurcation in resistive magnetohydrodynamics can be identified by starting from a particularly suitable form of the linearized equations which was previously introduced by the author as mentioned in this paper.