proposition 23.10 The characteristic function is the abbreviated action

open in the book · parts/03-classical-mechanics/06-hamilton-jacobi.tex:338 · p. 827

Rests on

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 ¶
      - depends_on definition 7.98 Functions of class $C^{1}$ ¶
      - depends_on definition 6.2 Open set ¶
  - 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 ¶

Supports

depends_on remark 23.11 Whose principle, and where it fails ¶

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
`depends_on`	→	Abbreviated action	declared	parts/03-classical-mechanics/06-hamilton-jacobi.tex:354
`depends_on`	→	Separation of the time	declared	parts/03-classical-mechanics/06-hamilton-jacobi.tex:354
`depends_on`	→	Maupertuis–Euler–Jacobi principle	declared	parts/03-classical-mechanics/06-hamilton-jacobi.tex:354
`depends_on`	←	Whose principle, and where it fails	declared	parts/03-classical-mechanics/06-hamilton-jacobi.tex:390
`proves`	←	ch:06-hamilton-jacobi@proof-4	declared	parts/03-classical-mechanics/06-hamilton-jacobi.tex:358