definition 23.39 Eikonal
open in the book ·
parts/03-classical-mechanics/06-hamilton-jacobi.tex:1230
· p. 837
- ground object -- no derivation owed
Rests on
-
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 ¶
Supports
-
depends_on
theorem 23.40
Eikonal and transport equations
¶
- 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 |
|---|---|---|---|---|
cites
(history) |
→ | Das Eikonal | derived | parts/03-classical-mechanics/06-hamilton-jacobi.tex:1246 |
cites
(history) |
→ | Theory of Systems of Rays | derived | parts/03-classical-mechanics/06-hamilton-jacobi.tex:1247 |
depends_on |
→ | Optical path length; Fermat's principle | declared | parts/03-classical-mechanics/06-hamilton-jacobi.tex:1248 |
depends_on |
→ | eq:pde-helmholtz-equation | declared | parts/03-classical-mechanics/06-hamilton-jacobi.tex:1248 |
depends_on |
← | Eikonal and transport equations | declared | parts/03-classical-mechanics/06-hamilton-jacobi.tex:1267 |