theorem 23.40 Eikonal and transport equations
open in the book ·
parts/03-classical-mechanics/06-hamilton-jacobi.tex:1251
· p. 838
Rests on
-
depends_on
definition 23.39
Eikonal
¶
-
depends_on
definition 16.103
Optical path length; Fermat's principle
¶
- depends_on equation 16.89 eq:calcvar-optical-length ¶
-
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 ¶
- depends_on equation 10.25 eq:pde-helmholtz-equation ¶
-
depends_on
definition 16.103
Optical path length; Fermat's principle
¶
- depends_on equation 23.63 eq:hj-helmholtz-medium ¶
- proves proof ch:06-hamilton-jacobi@proof-11 ¶
Supports
- depends_on proposition 23.41 Rays ¶
- depends_on remark 23.45 Why this is not an analogy ¶
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 |
→ | Eikonal | declared | parts/03-classical-mechanics/06-hamilton-jacobi.tex:1267 |
depends_on |
→ | eq:hj-helmholtz-medium | declared | parts/03-classical-mechanics/06-hamilton-jacobi.tex:1267 |
depends_on |
← | Rays | declared | parts/03-classical-mechanics/06-hamilton-jacobi.tex:1313 |
depends_on |
← | Why this is not an analogy | declared | parts/03-classical-mechanics/06-hamilton-jacobi.tex:1516 |
proves |
← | ch:06-hamilton-jacobi@proof-11 | declared | parts/03-classical-mechanics/06-hamilton-jacobi.tex:1270 |