The General Problem of the Stability of Motion.¶
Lyapunov, A. M. (1992). The General Problem of the Stability of Motion. Taylor & Francis.
Cited by¶
4 citations across 4 artifacts.
Each citation links to the sentence it supports in the citing article.
Primes¶
- Equilibrium
- Instability
- The foundational mathematical framework for stability analysis was established by Lyapunov's 1892 monograph
This sourceEstablishes the foundational framework for Lyapunov stability — the property that a reference trajectory remains in a small neighborhood of the initial state under infinitesimal perturbations. Introduces Lyapunov functions and Lyapunov exponents as tools for stability analysis without explicit solution of equations of motion. Cross-links with equilibrium stability (DP-11 G2).
- The foundational mathematical framework for stability analysis was established by Lyapunov's 1892 monograph
- Perturbation
- in long-term planetary motion. Stability probe. Perturbations serve as diagnostic tests of equilibrium and stability: small perturbations either decay (stable) or grow (unstable).
This sourceEstablishes the foundational framework for Lyapunov stability — the property that a reference trajectory remains in a small neighborhood of the initial state under infinitesimal perturbations. Introduces Lyapunov functions and Lyapunov exponents as tools for stability analysis without explicit solution of equations of motion. Cross-links with equilibrium stability (DP-11 G2).
- in long-term planetary motion. Stability probe. Perturbations serve as diagnostic tests of equilibrium and stability: small perturbations either decay (stable) or grow (unstable).
- Stability
- The pattern travels because the same triple — operating point, perturbation, restoring dynamics under intrinsic rules — recurs across control engineering, ecosystem dynamics, financial markets, political regimes, neural circuits, body temperature, and metabolic networks, with the Lyapunov framework as its canonical mathematical form.
This sourceThe canonical mathematical framework for stability of equilibria via Lyapunov functions.
- The pattern travels because the same triple — operating point, perturbation, restoring dynamics under intrinsic rules — recurs across control engineering, ecosystem dynamics, financial markets, political regimes, neural circuits, body temperature, and metabolic networks, with the Lyapunov framework as its canonical mathematical form.
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