definition 23.2 Hamilton's principal function and the Hamilton–Jacobi equation

open in the book · parts/03-classical-mechanics/06-hamilton-jacobi.tex:90 · p. 823

ground object -- no derivation owed

Rests on

depends_on equation 22.21 eq:ham-F2 ¶
depends_on equation 23.1 eq:hj-K-zero ¶
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 21.34 Generalized momentum ¶
      - depends_on definition 21.31 Lagrangian ¶
  - depends_on definition 21.45 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 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 ¶

Supports

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:ham-F2	declared	parts/03-classical-mechanics/06-hamilton-jacobi.tex:100
`depends_on`	→	eq:hj-K-zero	declared	parts/03-classical-mechanics/06-hamilton-jacobi.tex:100
`depends_on`	→	The mixed generating functions	declared	parts/03-classical-mechanics/06-hamilton-jacobi.tex:100
`depends_on`	←	Two functions, two roles	declared	parts/03-classical-mechanics/06-hamilton-jacobi.tex:399