theorem 22.38 Poisson's theorem
open in the book ·
parts/03-classical-mechanics/05-hamiltonian-mechanics.tex:1254
· p. 819
Rests on
- depends_on equation 22.46 eq:ham-jacobi ¶
-
depends_on
theorem 22.34
Evolution of a phase-space function
¶
- depends_on equation 22.4 eq:ham-pdot ¶
- depends_on equation 22.41 eq:ham-poisson-bracket ¶
- depends_on equation 22.3 eq:ham-qdot ¶
- proves proof ch:05-hamiltonian-mechanics@proof-14 ¶
- proves proof ch:05-hamiltonian-mechanics@proof-17 ¶
Supports
- depends_on proposition 25.12 The algebra of generators closes ¶
- depends_on remark 22.39 Poisson's theorem does not manufacture new constants ¶
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-jacobi | declared | parts/03-classical-mechanics/05-hamiltonian-mechanics.tex:1257 |
depends_on |
→ | Evolution of a phase-space function | declared | parts/03-classical-mechanics/05-hamiltonian-mechanics.tex:1257 |
depends_on |
← | The algebra of generators closes | declared | parts/03-classical-mechanics/08-poisson-quantum-bridge.tex:446 |
depends_on |
← | Poisson's theorem does not manufacture new constants | declared | parts/03-classical-mechanics/05-hamiltonian-mechanics.tex:1305 |
proves |
← | ch:05-hamiltonian-mechanics@proof-17 | declared | parts/03-classical-mechanics/05-hamiltonian-mechanics.tex:1260 |