definition 21.35 Cyclic coordinate
open in the book ·
parts/03-classical-mechanics/04-lagrangian-mechanics.tex:946
· p. 786
- ground object -- no derivation owed
Rests on
No declared or derived dependency edges point away from this node yet.
Supports
-
depends_on
proposition 23.14
Cyclic coordinates
¶
- 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 ¶
-
depends_on
theorem 21.36
Conservation of the conjugate momentum
¶
- depends_on proposition 23.14 Cyclic coordinates ¶ ↺
-
depends_on
proposition 29.36
Three first integrals
¶
- depends_on phenomenon 29.38 Nutation of a released top ¶
-
depends_on
proposition 29.43
The three integrable heavy tops
¶
- depends_on remark 29.45 What integrability buys, and where it stops ¶
- depends_on remark 29.44 The Kovalevskaya integral ¶
- depends_on proposition 29.40 The sleeping top ¶
-
depends_on
theorem 29.37
Reduction to one degree of freedom
¶
- depends_on phenomenon 29.38 Nutation of a released top ¶ ↺
- depends_on proposition 29.40 The sleeping top ¶ ↺
- depends_on remark 29.42 The closed form, and the mathematics it needs ¶
Neighborhood
Every logical edge within two steps of this node.
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- partly declared
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Edges
| type | direction | node | provenance | where |
|---|---|---|---|---|
depends_on |
← | Cyclic coordinates | declared | parts/03-classical-mechanics/06-hamilton-jacobi.tex:431 |
depends_on |
← | Conservation of the conjugate momentum | declared | parts/03-classical-mechanics/04-lagrangian-mechanics.tex:954 |