proposition 22.11 Hamiltonian and total energy
open in the book ·
parts/03-classical-mechanics/05-hamiltonian-mechanics.tex:304
· p. 808
Rests on
- depends_on equation 22.1 eq:ham-hamiltonian ¶
-
depends_on
proposition 21.38
Energy in generalized coordinates
¶
- depends_on equation 21.44 eq:lag-energy ¶
- depends_on equation 21.7 eq:lag-gct ¶
- depends_on equation 21.45 eq:lag-jacobi-integral ¶
- proves proof ch:04-lagrangian-mechanics@proof-9 ¶
- proves proof ch:05-hamiltonian-mechanics@proof-5 ¶
Supports
- depends_on remark 22.12 The hypothesis, stated sharply ¶
- depends_on remark 22.13 Euler's theorem on homogeneous functions is owed ¶
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-hamiltonian | declared | parts/03-classical-mechanics/05-hamiltonian-mechanics.tex:310 |
depends_on |
→ | Energy in generalized coordinates | declared | parts/03-classical-mechanics/05-hamiltonian-mechanics.tex:310 |
depends_on |
← | The hypothesis, stated sharply | declared | parts/03-classical-mechanics/05-hamiltonian-mechanics.tex:343 |
depends_on |
← | Euler's theorem on homogeneous functions is owed | declared | parts/03-classical-mechanics/05-hamiltonian-mechanics.tex:358 |
proves |
← | ch:05-hamiltonian-mechanics@proof-5 | declared | parts/03-classical-mechanics/05-hamiltonian-mechanics.tex:313 |