proposition 21.38 Energy in generalized coordinates
open in the book ·
parts/03-classical-mechanics/04-lagrangian-mechanics.tex:1011
· p. 787
Rests on
- 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 ¶
Supports
-
depends_on
proposition 22.11
Hamiltonian and total energy
¶
- 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:lag-energy | declared | parts/03-classical-mechanics/04-lagrangian-mechanics.tex:1020 |
depends_on |
→ | eq:lag-gct | declared | parts/03-classical-mechanics/04-lagrangian-mechanics.tex:1020 |
depends_on |
→ | eq:lag-jacobi-integral | declared | parts/03-classical-mechanics/04-lagrangian-mechanics.tex:1020 |
depends_on |
← | Hamiltonian and total energy | declared | parts/03-classical-mechanics/05-hamiltonian-mechanics.tex:310 |
proves |
← | ch:04-lagrangian-mechanics@proof-9 | declared | parts/03-classical-mechanics/04-lagrangian-mechanics.tex:1023 |