example 23.27 Charged particle in a uniform magnetic field

open in the book · parts/03-classical-mechanics/06-hamilton-jacobi.tex:859 · p. 833

example -- no derivation owed by its kind

Rests on

depends_on equation 23.49 eq:hj-action-variable ¶
depends_on proposition 23.14 Cyclic coordinates ¶
- 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 definition 21.35 Cyclic coordinate ¶
- depends_on theorem 21.36 Conservation of the conjugate momentum ¶
  - depends_on definition 21.35 Cyclic coordinate ¶ ↺
  - depends_on equation 21.39 eq:lag-el-conservative ¶
  - depends_on equation 21.43 eq:lag-generalized-momentum ¶
  - proves proof ch:04-lagrangian-mechanics@proof-8 ¶
- proves proof ch:06-hamilton-jacobi@proof-5 ¶
depends_on theorem 23.34 Adiabatic invariance of the action ¶
- 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 equation 22.10 eq:ham-dhdt ¶
- 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 21.45 Action ¶
      - depends_on theorem 22.6 Hamilton's equations ¶
    - 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 ¶
- proves proof ch:06-hamilton-jacobi@proof-9 ¶

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Edges

type	direction	node	provenance	where
`depends_on`	→	eq:hj-action-variable	declared	parts/03-classical-mechanics/06-hamilton-jacobi.tex:891
`depends_on`	→	Cyclic coordinates	declared	parts/03-classical-mechanics/06-hamilton-jacobi.tex:891
`depends_on`	→	Adiabatic invariance of the action	declared	parts/03-classical-mechanics/06-hamilton-jacobi.tex:891