proposition 23.9 Separation of the time

open in the book · parts/03-classical-mechanics/06-hamilton-jacobi.tex:303 · p. 826

Rests on

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 7.20 Continuity at a point ¶
      - depends_on definition 7.97 Partial derivative; gradient ¶
    - depends_on definition 6.2 Open set ¶
      - depends_on definition 6.1 Topological space ¶
- 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 ¶

Supports

depends_on proposition 23.10 The characteristic function is the abbreviated action ¶
- depends_on remark 23.11 Whose principle, and where it fails ¶
depends_on remark 23.12 Two functions, two roles ¶

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`	→	eq:hj-equation	declared	parts/03-classical-mechanics/06-hamilton-jacobi.tex:315
`depends_on`	→	The separation constant	declared	parts/03-classical-mechanics/06-hamilton-jacobi.tex:315
`depends_on`	→	Conservation of the Hamiltonian	declared	parts/03-classical-mechanics/06-hamilton-jacobi.tex:315
`depends_on`	←	The characteristic function is the abbreviated action	declared	parts/03-classical-mechanics/06-hamilton-jacobi.tex:354
`depends_on`	←	Two functions, two roles	declared	parts/03-classical-mechanics/06-hamilton-jacobi.tex:399
`proves`	←	ch:06-hamilton-jacobi@proof-3	declared	parts/03-classical-mechanics/06-hamilton-jacobi.tex:318