proposition 29.36 Three first integrals
open in the book ·
parts/03-classical-mechanics/12-rigid-body-rotating-frames.tex:1262
· p. 990
Rests on
- depends_on equation 29.35 eq:rigid-top-lagrangian ¶
-
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 ¶
-
depends_on
theorem 21.43
Conservation of energy
¶
- depends_on equation 21.51 eq:lag-energy-dot-cons ¶
- depends_on equation 21.46 eq:lag-energy-h ¶
-
depends_on
theorem 19.32
Conservation of energy
¶
-
depends_on
definition 19.31
Energy
¶
-
depends_on
definition 19.30
Conservative force and potential energy
¶
- depends_on equation 19.2 eq:newt-second-law ¶
- depends_on postulate 19.8 Newton's second law ¶
- depends_on definition 19.29 Kinetic energy ¶
-
depends_on
definition 19.30
Conservative force and potential energy
¶
- depends_on equation 19.19 eq:newt-conservative ¶
- depends_on equation 19.4 eq:newt-fma ¶
- proves proof ch:02-newtonian-dynamics@proof-9 ¶
-
depends_on
definition 19.31
Energy
¶
- proves proof ch:04-lagrangian-mechanics@proof-11 ¶
- proves proof ch:12-rigid-body-rotating-frames@proof-23 ¶
Supports
- 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.
- 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:rigid-top-lagrangian | declared | parts/03-classical-mechanics/12-rigid-body-rotating-frames.tex:1276 |
depends_on |
→ | Conservation of the conjugate momentum | declared | parts/03-classical-mechanics/12-rigid-body-rotating-frames.tex:1276 |
depends_on |
→ | Conservation of energy | declared | parts/03-classical-mechanics/12-rigid-body-rotating-frames.tex:1276 |
depends_on |
← | Nutation of a released top | declared | parts/03-classical-mechanics/12-rigid-body-rotating-frames.tex:1363 |
depends_on |
← | The three integrable heavy tops | declared | parts/03-classical-mechanics/12-rigid-body-rotating-frames.tex:1591 |
depends_on |
← | The sleeping top | declared | parts/03-classical-mechanics/12-rigid-body-rotating-frames.tex:1461 |
depends_on |
← | Reduction to one degree of freedom | declared | parts/03-classical-mechanics/12-rigid-body-rotating-frames.tex:1321 |
proves |
← | ch:12-rigid-body-rotating-frames@proof-23 | declared | parts/03-classical-mechanics/12-rigid-body-rotating-frames.tex:1280 |