theorem 29.37 Reduction to one degree of freedom

open in the book · parts/03-classical-mechanics/12-rigid-body-rotating-frames.tex:1297 · p. 991

Rests on

depends_on proposition 29.36 Three first integrals ¶
- 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 definition 19.29 Kinetic 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 ¶
  - proves proof ch:04-lagrangian-mechanics@proof-11 ¶
- proves proof ch:12-rigid-body-rotating-frames@proof-23 ¶
depends_on theorem 7.23 Intermediate value theorem ¶
- depends_on axiom 7.1 Completeness of $\R$ ¶
- depends_on definition 7.20 Continuity at a point ¶
  - depends_on definition 7.16 Limit ¶
    - depends_on definition 7.2 Absolute value ¶
    - depends_on definition 7.9 Real function ¶
      - depends_on definition 3.43 Map ¶
  - depends_on equation 7.7 eq:ana-limit-left ¶
  - depends_on equation 7.5 eq:ana-limit-right ¶
- proves proof ch:05-real-analysis@proof-8 ¶
proves proof ch:12-rigid-body-rotating-frames@proof-24 ¶

Supports

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`	→	Three first integrals	declared	parts/03-classical-mechanics/12-rigid-body-rotating-frames.tex:1321
`depends_on`	→	Intermediate value theorem	declared	parts/03-classical-mechanics/12-rigid-body-rotating-frames.tex:1321
`depends_on`	←	Nutation of a released top	declared	parts/03-classical-mechanics/12-rigid-body-rotating-frames.tex:1363
`depends_on`	←	The sleeping top	declared	parts/03-classical-mechanics/12-rigid-body-rotating-frames.tex:1461
`depends_on`	←	The closed form, and the mathematics it needs	declared	parts/03-classical-mechanics/12-rigid-body-rotating-frames.tex:1558
`proves`	←	ch:12-rigid-body-rotating-frames@proof-24	declared	parts/03-classical-mechanics/12-rigid-body-rotating-frames.tex:1324