theorem 16.101 Maupertuis–Euler–Jacobi principle
open in the book ·
parts/02-mathematical-methods/14-calculus-of-variations.tex:3195
· p. 666
Rests on
- depends_on equation 16.88 eq:calcvar-abbreviated ¶
- depends_on equation 16.87 eq:calcvar-newton ¶
-
depends_on
lemma 16.100
The ray equation
¶
- depends_on equation 16.30 eq:calcvar-euler-lagrange-system ¶
- depends_on equation 16.89 eq:calcvar-optical-length ¶
- proves proof ch:14-calculus-of-variations@proof-47 ¶
- proves proof ch:14-calculus-of-variations@proof-48 ¶
Supports
-
depends_on
proposition 23.10
The characteristic function is the abbreviated action
¶
- depends_on remark 23.11 Whose principle, and where it fails ¶
- depends_on remark 23.11 Whose principle, and where it fails ¶ ↺
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-abbreviated | declared | parts/02-mathematical-methods/14-calculus-of-variations.tex:3210 |
depends_on |
→ | eq:calcvar-newton | declared | parts/02-mathematical-methods/14-calculus-of-variations.tex:3210 |
depends_on |
→ | The ray equation | declared | parts/02-mathematical-methods/14-calculus-of-variations.tex:3210 |
depends_on |
← | The characteristic function is the abbreviated action | declared | parts/03-classical-mechanics/06-hamilton-jacobi.tex:354 |
depends_on |
← | Whose principle, and where it fails | declared | parts/03-classical-mechanics/06-hamilton-jacobi.tex:390 |
proves |
← | ch:14-calculus-of-variations@proof-48 | declared | parts/02-mathematical-methods/14-calculus-of-variations.tex:3214 |