The General Problem of the Stability of Motion

Lyapunov, A. M. (1892). The General Problem of the Stability of Motion.

Type

Book

Intellectual base

Review or monograph

Year

1892

Link

no authoritative link yet

Cited from

physics

Cited by

2 citations across 2 artifacts.

Each citation links to the sentence it supports in the citing article.

Primes

• 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).

• 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).

Verification

This reference passed the adversarial substantiation pipeline: it was checked to exist and to support the claim it is attached to. See how references were verified.

Registry ID ref:9b170325d644 · see in the full table