equation 16.20 eq:calcvar-euler-lagrange
open in the book ·
parts/02-mathematical-methods/14-calculus-of-variations.tex:650
- part of a statement or proof
Rests on
No declared or derived dependency edges point away from this node yet.
Supports
-
depends_on
corollary 16.23
du Bois-Reymond form
¶
-
depends_on
corollary 16.33
Weierstrass–Erdmann corner conditions
¶
-
depends_on
theorem 16.55
Jacobi's necessary condition
¶
- depends_on proposition 23.53 A caustic point is a conjugate point ¶
- depends_on remark 30.54 Other end conditions, and what buckling is variationally ¶
-
depends_on
theorem 16.55
Jacobi's necessary condition
¶
-
depends_on
corollary 16.33
Weierstrass–Erdmann corner conditions
¶
-
depends_on
definition 16.53
Jacobi accessory equation; conjugate point
¶
- depends_on proposition 23.53 A caustic point is a conjugate point ¶ ↺
-
depends_on
theorem A.436
Strengthened Jacobi condition and conjugate points
¶
- depends_on corollary A.445 Displacing the initial point ¶
- depends_on theorem 16.55 Jacobi's necessary condition ¶ ↺
-
depends_on
proposition 16.28
Cyclic coordinate
¶
-
depends_on
corollary 16.88
Momentum and angular momentum
¶
- depends_on example 28.39 The linear triatomic molecule ¶
-
depends_on
corollary 16.88
Momentum and angular momentum
¶
- depends_on proposition 16.26 Covariance under change of dependent variable ¶
-
depends_on
theorem 16.29
Beltrami identity
¶
- depends_on proposition 16.105 The optical invariant in a stratified medium ¶
- depends_on proposition 16.39 Ostrogradsky instability ¶
-
depends_on
theorem 16.63
Hilbert's invariant integral
¶
- depends_on remark 23.8 The action as a function, not a functional ¶
- depends_on theorem 16.64 Weierstrass' sufficient condition ¶
-
depends_on
theorem 16.32
Transversality
¶
- depends_on corollary 16.33 Weierstrass–Erdmann corner conditions ¶ ↺
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 |
← | du Bois-Reymond form | declared | parts/02-mathematical-methods/14-calculus-of-variations.tex:685 |
depends_on |
← | Jacobi accessory equation; conjugate point | declared | parts/02-mathematical-methods/14-calculus-of-variations.tex:1600 |
depends_on |
← | Cyclic coordinate | declared | parts/02-mathematical-methods/14-calculus-of-variations.tex:802 |
depends_on |
← | Covariance under change of dependent variable | declared | parts/02-mathematical-methods/14-calculus-of-variations.tex:746 |
depends_on |
← | Beltrami identity | declared | parts/02-mathematical-methods/14-calculus-of-variations.tex:819 |
depends_on |
← | Hilbert's invariant integral | declared | parts/02-mathematical-methods/14-calculus-of-variations.tex:1881 |
depends_on |
← | Transversality | declared | parts/02-mathematical-methods/14-calculus-of-variations.tex:891 |