proposition 22.17 Transformation conditions

open in the book · parts/03-classical-mechanics/05-hamiltonian-mechanics.tex:410 · p. 809

Rests on

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 22.14 eq:ham-ct-P ¶
depends_on equation 22.13 eq:ham-ct-Q ¶
proves proof ch:05-hamiltonian-mechanics@proof-8 ¶

Supports

depends_on remark 22.21 The count ¶

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`	→	Canonical transformation	declared	parts/03-classical-mechanics/05-hamiltonian-mechanics.tex:423
`depends_on`	→	eq:ham-ct-P	declared	parts/03-classical-mechanics/05-hamiltonian-mechanics.tex:423
`depends_on`	→	eq:ham-ct-Q	declared	parts/03-classical-mechanics/05-hamiltonian-mechanics.tex:423
`depends_on`	←	The count	declared	parts/03-classical-mechanics/05-hamiltonian-mechanics.tex:711
`proves`	←	ch:05-hamiltonian-mechanics@proof-8	declared	parts/03-classical-mechanics/05-hamiltonian-mechanics.tex:665