example 32.21 The damped pendulum

open in the book · parts/03-classical-mechanics/15-nonlinear-dynamics-chaos.tex:481 · p. 1086

example -- no derivation owed by its kind

Rests on

depends_on equation 28.8 eq:osc-pendulum-exact ¶
depends_on theorem 32.20 Lyapunov's direct method ¶
- depends_on definition 32.19 Lyapunov function ¶
  - depends_on definition 7.97 Partial derivative; gradient ¶
    - depends_on definition 7.26 Derivative of a function at a point ¶
      - depends_on definition 7.16 Limit ¶
      - depends_on definition 7.9 Real function ¶
    - depends_on definition 5.15 Basis ¶
      - depends_on definition 5.12 Subspace generated by a set of vectors ¶
      - depends_on definition 5.14 Linear independence ¶
  - 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 9.1 Ordinary differential equation ¶
- depends_on definition 32.11 Lyapunov stability ¶
  - depends_on definition 32.10 Fixed point ¶ ↺
- proves proof ch:15-nonlinear-dynamics-chaos@proof-6 ¶

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type	direction	node	provenance	where
`depends_on`	→	eq:osc-pendulum-exact	declared	parts/03-classical-mechanics/15-nonlinear-dynamics-chaos.tex:509
`depends_on`	→	Lyapunov's direct method	declared	parts/03-classical-mechanics/15-nonlinear-dynamics-chaos.tex:509