proposition 16.17 The first variation of an integral functional
open in the book ·
parts/02-mathematical-methods/14-calculus-of-variations.tex:495
· p. 636
Rests on
- 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 ¶
Supports
-
depends_on
theorem 16.43
Euler's rule for integral constraints
¶
- depends_on example 16.45 Two solved isoperimetric problems ¶
- depends_on proposition 16.4 The hanging chain is a catenary ¶
- depends_on proposition 16.6 The isoperimetric extremal is a circle ¶
-
depends_on
theorem 16.84
Noether's first theorem, one independent variable
¶
-
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
theorem 16.93
Noether's second theorem
¶
-
depends_on
theorem 16.90
Noether's first theorem, several independent variables
¶
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-basic-functional | declared | parts/02-mathematical-methods/14-calculus-of-variations.tex:506 |
depends_on |
→ | eq:calcvar-gateaux | declared | parts/02-mathematical-methods/14-calculus-of-variations.tex:506 |
depends_on |
← | Euler's rule for integral constraints | declared | parts/02-mathematical-methods/14-calculus-of-variations.tex:1292 |
depends_on |
← | Noether's first theorem, one independent variable | declared | parts/02-mathematical-methods/14-calculus-of-variations.tex:2680 |
proves |
← | ch:14-calculus-of-variations@proof-7 | declared | parts/02-mathematical-methods/14-calculus-of-variations.tex:509 |