then the solution is called linearly stable. Other names for linear stability include exponential stability or stability in terms of first approximation...
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interest. In the study of dynamical systems, linearization is a method for assessing the local stability of an equilibrium point of a system of nonlinear...
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Linear stability Orbital stability Stability criterion Stability radius Structural stability von Neumann stability analysis Egwald Mathematics - Linear Algebra:...
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{\displaystyle {\mathcal {A}}\,} is the Atwood number. Details of the linear stability analysis. A similar derivation appears in Chandrasekhar 1981, §92,...
28 KB (4,053 words) - 07:55, 19 September 2023
dynamical systems Asymptotic stability Linear stability Lyapunov stability Orbital stability Structural stability Stability (probability), a property of...
4 KB (487 words) - 09:36, 3 January 2024
formalize the concept of stability. The following definitions of forward, backward, and mixed stability are often used in numerical linear algebra. Consider...
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hydrodynamic stability is the field which analyses the stability and the onset of instability of fluid flows. The study of hydrodynamic stability aims to find...
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definitions through which it may be assessed: BIBO stability Linear stability Lyapunov stability Orbital stability This article includes a list of related items...
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extended Plateau's work to consider the linear stability of viscous threads. Rayleigh solved for the stability of a viscous thread of viscosity μ A {\displaystyle...
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Nonlinear control (redirect from Non-linear control)
sufficient conditions for absolute stability: The circle criterion (an extension of the Nyquist stability criterion for linear systems) The Popov criterion...
12 KB (1,328 words) - 20:01, 14 January 2024
Equilibrium point (mathematics) (category Stability theory)
point Steady state Egwald Mathematics - Linear Algebra: Systems of Linear Differential Equations: Linear Stability Analysis Accessed 10 October 2019. Boyce...
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feedback. While Nyquist is one of the most general stability tests, it is still restricted to linear time-invariant (LTI) systems. Nevertheless, there...
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diagrams, it is also possible to demonstrate the stability of various fixed points using linear stability analysis. First, find the fixed points in the phase...
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Trehan (S.K. Trehan) was an Indian mathematician who specialised in non-linear stability in magnetohydrodynamics. He was awarded in 1976 the Shanti Swarup Bhatnagar...
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become unstable in the presence of diffusion. A linear stability analysis however shows that when linearizing the general two-component system ( ∂ t u ∂ t...
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Euler method (section Numerical stability)
1{\bigr \}},} illustrated on the right. This region is called the (linear) stability region. In the example, k = − 2.3 {\displaystyle k=-2.3} , so if h...
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to the analysis of the stability of nonlinear dynamical systems by comparison with the widely spread local method of linearizing them about points of equilibrium...
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system (mathematics) Egwald Mathematics - Linear Algebra: Systems of Linear Differential Equations: Linear Stability Analysis Accessed 10 October 2019. Boyce...
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the initial disturbances grow (or decay) in a manner described by linear stability theory. The specific instabilities that are exhibited in reality depend...
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conjecture on absolute stability of nonlinear control system with one scalar nonlinearity, which belongs to the sector of linear stability. Kalman's conjecture...
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t\in \mathbb {R} } For a continuous time linear time-invariant (LTI) system, the condition for BIBO stability is that the impulse response, h ( t ) {\displaystyle...
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Newmark-beta method (section Stability Analysis)
t ) {\displaystyle q_{n+1}=A(\Delta t)q_{n}+g_{n+1}(\Delta t)} The linear stability is equivalent to ρ ( A ( Δ t ) ) ≤ 1 {\displaystyle \rho (A(\Delta...
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analysis, von Neumann stability analysis (also known as Fourier stability analysis) is a procedure used to check the stability of finite difference schemes...
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Aizerman's conjecture such that nonlinearity belongs to the sector of linear stability and unique stable equilibrium coexists with a stable periodic solution...
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ISBN 978-0-691-08777-1. Hintz, Peter; Vasy, András (2018). "The global non-linear stability of the Kerr-de Sitter family of black holes". Acta Mathematica. 220...
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the Routh–Hurwitz stability criterion is a mathematical test that is a necessary and sufficient condition for the stability of a linear time-invariant (LTI)...
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chosen sufficiently large. Stability theory Asymptotic stability Linear stability Lyapunov stability Vakhitov−Kolokolov stability criterion Manoussos Grillakis;...
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changes and oscillations. Stability and control derivatives are used to linearize (simplify) these equations of motion so the stability of the vehicle can be...
20 KB (3,324 words) - 01:23, 3 September 2023
In the theory of dynamical systems and control theory, a linear time-invariant system is marginally stable if it is neither asymptotically stable nor unstable...
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In solid mechanics, the linear stability analysis of an elastic solution is studied using the method of incremental deformations superposed on finite deformations...
19 KB (2,954 words) - 02:05, 1 November 2023