theorem 23.17 Stäckel's conditions are sufficient
open in the book ·
parts/03-classical-mechanics/06-hamilton-jacobi.tex:503
· p. 829
Rests on
-
depends_on
definition 23.13
Additive separability
¶
-
depends_on
definition 23.5
Complete integral
¶
- depends_on equation 23.2 eq:hj-equation ¶
- depends_on equation 23.15 eq:hj-characteristic-equation ¶
-
depends_on
definition 23.5
Complete integral
¶
-
depends_on
definition 23.16
Stäckel matrix; Stäckel system
¶
- depends_on equation 23.23 eq:hj-orthogonal-hamiltonian ¶
- depends_on equation 23.15 eq:hj-characteristic-equation ¶ ↺
- proves proof ch:06-hamilton-jacobi@proof-6 ¶
Supports
- depends_on remark 23.18 The converse, and what this treatise does not prove ¶
- depends_on remark 23.19 The same conditions govern the Helmholtz equation ¶
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 |
→ | Additive separability | declared | parts/03-classical-mechanics/06-hamilton-jacobi.tex:513 |
depends_on |
→ | Stäckel matrix; Stäckel system | declared | parts/03-classical-mechanics/06-hamilton-jacobi.tex:513 |
depends_on |
→ | eq:hj-characteristic-equation | declared | parts/03-classical-mechanics/06-hamilton-jacobi.tex:513 |
depends_on |
← | The converse, and what this treatise does not prove | declared | parts/03-classical-mechanics/06-hamilton-jacobi.tex:592 |
depends_on |
← | The same conditions govern the Helmholtz equation | declared | parts/03-classical-mechanics/06-hamilton-jacobi.tex:617 |
proves |
← | ch:06-hamilton-jacobi@proof-6 | declared | parts/03-classical-mechanics/06-hamilton-jacobi.tex:516 |