example 23.24 Harmonic oscillator

open in the book · parts/03-classical-mechanics/06-hamilton-jacobi.tex:755 · p. 832

example -- no derivation owed by its kind

Rests on

depends_on definition 23.28 Action variables ¶
- depends_on definition 16.99 Abbreviated action ¶
  - depends_on definition 16.96 Action; Hamilton's principle ¶
    - depends_on definition 21.31 Lagrangian ¶
    - depends_on equation 16.11 eq:calcvar-basic-functional ¶
  - depends_on equation 16.86 eq:calcvar-hamilton-action ¶
- depends_on definition 23.13 Additive separability ¶
  - depends_on definition 23.5 Complete integral ¶
    - depends_on equation 23.2 eq:hj-equation ¶
  - depends_on equation 23.15 eq:hj-characteristic-equation ¶
depends_on proposition 28.6 Phase-space area and the action variable ¶
- depends_on equation 28.5 eq:osc-energy ¶
- depends_on equation 28.3 eq:osc-lagrangian ¶
- proves proof ch:11-oscillations-waves@proof-3 ¶
depends_on theorem 23.30 Motion in action–angle variables ¶
- depends_on definition 23.28 Action variables ¶ ↺
- depends_on proposition 22.18 The mixed generating functions ¶
  - depends_on definition 22.15 Canonical transformation ¶
    - depends_on definition 22.14 Phase-space coordinate transformation ¶
      - depends_on definition 22.2 Hamiltonian ¶
    - depends_on definition 21.45 Action ¶
      - depends_on definition 16.96 Action; Hamilton's principle ¶ ↺
      - depends_on equation 21.37 eq:lag-lagrangian ¶
    - depends_on theorem 22.6 Hamilton's equations ¶
      - depends_on definition 22.2 Hamiltonian ¶ ↺
      - depends_on equation 21.39 eq:lag-el-conservative ¶
      - depends_on equation 21.43 eq:lag-generalized-momentum ¶
      - proves proof ch:05-hamiltonian-mechanics@proof-2 ¶
  - depends_on equation 22.18 eq:ham-generating ¶
  - proves proof ch:05-hamiltonian-mechanics@proof-6 ¶
- depends_on theorem 22.6 Hamilton's equations ¶ ↺
- proves proof ch:06-hamilton-jacobi@proof-8 ¶

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type	direction	node	provenance	where
`depends_on`	→	Action variables	declared	parts/03-classical-mechanics/06-hamilton-jacobi.tex:774
`depends_on`	→	Phase-space area and the action variable	declared	parts/03-classical-mechanics/06-hamilton-jacobi.tex:774
`depends_on`	→	Motion in action–angle variables	declared	parts/03-classical-mechanics/06-hamilton-jacobi.tex:774