proposition 23.14 Cyclic coordinates
open in the book ·
parts/03-classical-mechanics/06-hamilton-jacobi.tex:423
· p. 828
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 21.35 Cyclic coordinate ¶
-
depends_on
theorem 21.36
Conservation of the conjugate momentum
¶
- depends_on definition 21.35 Cyclic coordinate ¶ ↺
- depends_on equation 21.39 eq:lag-el-conservative ¶
- depends_on equation 21.43 eq:lag-generalized-momentum ¶
- proves proof ch:04-lagrangian-mechanics@proof-8 ¶
- proves proof ch:06-hamilton-jacobi@proof-5 ¶
Supports
- depends_on example 23.25 Central force in plane polar coordinates ¶
-
depends_on
example 23.22
Free particle
¶
- depends_on remark 23.42 Phase speed and particle speed ¶
- depends_on example 23.27 Charged particle in a uniform magnetic field ¶
- depends_on example 23.23 Uniform gravity, and the parabola ¶
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:431 |
depends_on |
→ | Cyclic coordinate | declared | parts/03-classical-mechanics/06-hamilton-jacobi.tex:431 |
depends_on |
→ | Conservation of the conjugate momentum | declared | parts/03-classical-mechanics/06-hamilton-jacobi.tex:431 |
depends_on |
← | Central force in plane polar coordinates | declared | parts/03-classical-mechanics/06-hamilton-jacobi.tex:804 |
depends_on |
← | Free particle | declared | parts/03-classical-mechanics/06-hamilton-jacobi.tex:724 |
depends_on |
← | Charged particle in a uniform magnetic field | declared | parts/03-classical-mechanics/06-hamilton-jacobi.tex:891 |
depends_on |
← | Uniform gravity, and the parabola | declared | parts/03-classical-mechanics/06-hamilton-jacobi.tex:752 |
proves |
← | ch:06-hamilton-jacobi@proof-5 | declared | parts/03-classical-mechanics/06-hamilton-jacobi.tex:434 |