lemma 16.100 The ray equation

open in the book · parts/02-mathematical-methods/14-calculus-of-variations.tex:3158 · p. 666

Rests on

depends_on definition 16.103 Optical path length; Fermat's principle ¶
- depends_on definition 23.39 Eikonal ¶
  - 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 ¶
- depends_on proposition 23.41 Rays ¶ ↺
- depends_on theorem 16.104 Snell's law of refraction ¶
depends_on proposition 23.41 Rays ¶ ↺
depends_on theorem 16.101 Maupertuis–Euler–Jacobi principle ¶
- 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 ¶ ↺

Every logical edge within two steps of this node.

type	direction	node	provenance	where
`depends_on`	→	eq:calcvar-euler-lagrange-system	declared	parts/02-mathematical-methods/14-calculus-of-variations.tex:3173
`depends_on`	→	eq:calcvar-optical-length	declared	parts/02-mathematical-methods/14-calculus-of-variations.tex:3173
`depends_on`	←	Optical path length; Fermat's principle	declared	parts/02-mathematical-methods/14-calculus-of-variations.tex:3287
`depends_on`	←	Rays	declared	parts/03-classical-mechanics/06-hamilton-jacobi.tex:1313
`depends_on`	←	Maupertuis–Euler–Jacobi principle	declared	parts/02-mathematical-methods/14-calculus-of-variations.tex:3210
`proves`	←	ch:14-calculus-of-variations@proof-47	declared	parts/02-mathematical-methods/14-calculus-of-variations.tex:3177