proposition 23.49 The Hamilton–Jacobi equation is the leading order
open in the book ·
parts/03-classical-mechanics/06-hamilton-jacobi.tex:1645
· p. 842
Rests on
- depends_on equation 23.72 eq:hj-mechanical-eikonal ¶
- depends_on equation 23.66 eq:hj-transport ¶
-
depends_on
proposition 9.61
Eikonal and transport equations
¶
- depends_on equation 9.64 eq:slt-wkb-series ¶
-
depends_on
proposition 9.60
Exact Riccati form
¶
- depends_on equation 9.62 eq:slt-wkb-ansatz ¶
- depends_on equation 9.60 eq:slt-wkb-normal-form ¶
- proves proof ch:07-odes-sturm-liouville@proof-30 ¶
- proves proof ch:07-odes-sturm-liouville@proof-31 ¶
- proves proof ch:06-hamilton-jacobi@proof-15 ¶
Supports
- depends_on remark 23.50 The dictionary completed ¶
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:hj-mechanical-eikonal | declared | parts/03-classical-mechanics/06-hamilton-jacobi.tex:1674 |
depends_on |
→ | eq:hj-transport | declared | parts/03-classical-mechanics/06-hamilton-jacobi.tex:1674 |
depends_on |
→ | Eikonal and transport equations | declared | parts/03-classical-mechanics/06-hamilton-jacobi.tex:1674 |
depends_on |
← | The dictionary completed | declared | parts/03-classical-mechanics/06-hamilton-jacobi.tex:1735 |
proves |
← | ch:06-hamilton-jacobi@proof-15 | declared | parts/03-classical-mechanics/06-hamilton-jacobi.tex:1677 |