proposition 23.41 Rays

open in the book · parts/03-classical-mechanics/06-hamilton-jacobi.tex:1303 · p. 838

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 lemma 16.100 The ray equation ¶ ↺
depends_on theorem 23.40 Eikonal and transport equations ¶
- depends_on definition 23.39 Eikonal ¶
  - depends_on definition 16.103 Optical path length; Fermat's principle ¶ ↺
  - depends_on equation 10.25 eq:pde-helmholtz-equation ¶
- depends_on equation 23.63 eq:hj-helmholtz-medium ¶
- proves proof ch:06-hamilton-jacobi@proof-11 ¶
proves proof ch:06-hamilton-jacobi@proof-12 ¶

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type	direction	node	provenance	where
`depends_on`	→	Optical path length; Fermat's principle	declared	parts/03-classical-mechanics/06-hamilton-jacobi.tex:1313
`depends_on`	→	The ray equation	declared	parts/03-classical-mechanics/06-hamilton-jacobi.tex:1313
`depends_on`	→	Eikonal and transport equations	declared	parts/03-classical-mechanics/06-hamilton-jacobi.tex:1313
`proves`	←	ch:06-hamilton-jacobi@proof-12	declared	parts/03-classical-mechanics/06-hamilton-jacobi.tex:1316