theorem 22.34 Evolution of a phase-space function
open in the book ·
parts/03-classical-mechanics/05-hamiltonian-mechanics.tex:1172
· p. 818
Rests on
- 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 ¶
Supports
-
depends_on
corollary 22.35
cor:ham-evolution-static
¶
- depends_on proposition 22.37 Constants of motion ¶
- depends_on remark 22.36 The whole dynamics in one operation ¶
-
depends_on
theorem 22.38
Poisson's theorem
¶
- 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-pdot | declared | parts/03-classical-mechanics/05-hamiltonian-mechanics.tex:1177 |
depends_on |
→ | eq:ham-poisson-bracket | declared | parts/03-classical-mechanics/05-hamiltonian-mechanics.tex:1177 |
depends_on |
→ | eq:ham-qdot | declared | parts/03-classical-mechanics/05-hamiltonian-mechanics.tex:1177 |
depends_on |
← | cor:ham-evolution-static | declared | parts/03-classical-mechanics/05-hamiltonian-mechanics.tex:1199 |
depends_on |
← | The whole dynamics in one operation | declared | parts/03-classical-mechanics/05-hamiltonian-mechanics.tex:1223 |
depends_on |
← | Poisson's theorem | declared | parts/03-classical-mechanics/05-hamiltonian-mechanics.tex:1257 |
proves |
← | ch:05-hamiltonian-mechanics@proof-14 | declared | parts/03-classical-mechanics/05-hamiltonian-mechanics.tex:1180 |