remark 23.11 Whose principle, and where it fails

open in the book · parts/03-classical-mechanics/06-hamilton-jacobi.tex:378 · p. 827

remark -- no derivation owed by its kind

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depends_on proposition 23.10 The characteristic function is the abbreviated action ¶
- 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 proposition 23.9 Separation of the time ¶
  - depends_on equation 23.2 eq:hj-equation ¶
  - depends_on lemma 10.28 The separation constant ¶
    - depends_on definition 10.2 Linear, semilinear, quasilinear ¶
      - depends_on definition 10.1 Partial differential equation; order ¶
    - proves proof ch:08-pdes@proof-9 ¶
  - depends_on theorem 22.10 Conservation of the Hamiltonian ¶
    - depends_on proposition 22.9 Time derivative of the Hamiltonian ¶
      - depends_on equation 22.4 eq:ham-pdot ¶
      - depends_on equation 22.3 eq:ham-qdot ¶
      - proves proof ch:05-hamiltonian-mechanics@proof-3 ¶
    - proves proof ch:05-hamiltonian-mechanics@proof-4 ¶
  - proves proof ch:06-hamilton-jacobi@proof-3 ¶
- depends_on theorem 16.101 Maupertuis–Euler–Jacobi principle ¶
  - depends_on equation 16.88 eq:calcvar-abbreviated ¶
  - depends_on equation 16.87 eq:calcvar-newton ¶
  - depends_on lemma 16.100 The ray equation ¶
    - depends_on equation 16.30 eq:calcvar-euler-lagrange-system ¶
    - depends_on equation 16.89 eq:calcvar-optical-length ¶
    - proves proof ch:14-calculus-of-variations@proof-47 ¶
  - proves proof ch:14-calculus-of-variations@proof-48 ¶
- proves proof ch:06-hamilton-jacobi@proof-4 ¶
depends_on theorem 16.101 Maupertuis–Euler–Jacobi principle ¶ ↺

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`cites` (history)	→	Methodus inveniendi lineas curvas maximi minimive proprietate gaudentes, sive solutio problematis isoperimetrici latissimo sensu accepti	derived	parts/03-classical-mechanics/06-hamilton-jacobi.tex:382
`cites` (history)	→	Les loix du mouvement et du repos déduites d'un principe métaphysique	derived	parts/03-classical-mechanics/06-hamilton-jacobi.tex:383
`depends_on`	→	The characteristic function is the abbreviated action	declared	parts/03-classical-mechanics/06-hamilton-jacobi.tex:390
`depends_on`	→	Maupertuis–Euler–Jacobi principle	declared	parts/03-classical-mechanics/06-hamilton-jacobi.tex:390