definition 32.11 Lyapunov stability
open in the book ·
parts/03-classical-mechanics/15-nonlinear-dynamics-chaos.tex:254
· p. 1083
- ground object -- no derivation owed
Rests on
-
depends_on
definition 32.10
Fixed point
¶
-
depends_on
definition 32.3
Dynamical system, phase space, flow
¶
-
depends_on
definition 13.82
Vector field
¶
-
depends_on
definition 13.81
Vector on a manifold
¶
- depends_on definition 13.71 Differentiable curve ¶
- depends_on definition 13.45 Differentiable map on a topological space ¶
- depends_on definition 13.48 Differentiable manifold ¶
-
depends_on
definition 13.81
Vector on a manifold
¶
- depends_on definition 9.1 Ordinary differential equation ¶
-
depends_on
definition 13.82
Vector field
¶
-
depends_on
definition 32.3
Dynamical system, phase space, flow
¶
Supports
-
depends_on
theorem 32.20
Lyapunov's direct method
¶
- depends_on example 32.21 The damped pendulum ¶
Neighborhood
Every logical edge within two steps of this node.
- declared and complete
- partly declared
- a check failed
- not graded
- declared in the source
- inferred from structure
Edges
| type | direction | node | provenance | where |
|---|---|---|---|---|
cites |
→ | Obshchaya zadacha ob ustoichivosti dvizheniya (The General Problem of the Stability of Motion) | derived | parts/03-classical-mechanics/15-nonlinear-dynamics-chaos.tex:261 |
depends_on |
→ | Fixed point | declared | parts/03-classical-mechanics/15-nonlinear-dynamics-chaos.tex:262 |
depends_on |
← | Lyapunov's direct method | declared | parts/03-classical-mechanics/15-nonlinear-dynamics-chaos.tex:460 |