theorem 16.84 Noether's first theorem, one independent variable
open in the book ·
parts/02-mathematical-methods/14-calculus-of-variations.tex:2668
· p. 661
Rests on
- depends_on equation 16.30 eq:calcvar-euler-lagrange-system ¶
- depends_on equation 16.75 eq:calcvar-invariance ¶
-
depends_on
proposition 16.17
The first variation of an integral functional
¶
- depends_on equation 16.11 eq:calcvar-basic-functional ¶
- depends_on equation 16.14 eq:calcvar-gateaux ¶
- proves proof ch:14-calculus-of-variations@proof-7 ¶
- proves proof ch:14-calculus-of-variations@proof-39 ¶
Supports
-
depends_on
theorem 16.90
Noether's first theorem, several independent variables
¶
-
depends_on
theorem 16.93
Noether's second theorem
¶
- depends_on example 16.109 The Einstein–Hilbert action ¶
-
depends_on
theorem 44.19
Covariant conservation of stress–energy
¶
-
depends_on
proposition 44.20
Perfect-fluid equations of motion
¶
- depends_on corollary 44.21 Dust flows on geodesics ¶
-
depends_on
proposition 44.20
Perfect-fluid equations of motion
¶
-
depends_on
theorem 16.93
Noether's second theorem
¶
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:calcvar-euler-lagrange-system | declared | parts/02-mathematical-methods/14-calculus-of-variations.tex:2680 |
depends_on |
→ | eq:calcvar-invariance | declared | parts/02-mathematical-methods/14-calculus-of-variations.tex:2680 |
depends_on |
→ | The first variation of an integral functional | declared | parts/02-mathematical-methods/14-calculus-of-variations.tex:2680 |
depends_on |
← | Noether's first theorem, several independent variables | declared | parts/02-mathematical-methods/14-calculus-of-variations.tex:2869 |
proves |
← | ch:14-calculus-of-variations@proof-39 | declared | parts/02-mathematical-methods/14-calculus-of-variations.tex:2684 |