theorem 29.7 Transport theorem

open in the book · parts/03-classical-mechanics/12-rigid-body-rotating-frames.tex:167 · p. 978

Rests on

depends_on definition 29.4 Angular velocity ¶
- depends_on definition 14.26 The rotation group ¶
- depends_on lemma 14.62 The Levi-Civita symbol is invariant ¶
  - depends_on equation 13.223 eq:mfd-epsilon-density ¶
  - depends_on example 13.94 The two densities this chapter uses ¶
    - depends_on definition 13.92 Tensor density ¶
      - depends_on definition 13.89 Contravariant and covariant tensors ¶
      - depends_on definition 13.88 General coordinate transformation ¶
    - depends_on proposition 13.93 Algebra of densities ¶
      - depends_on definition 13.92 Tensor density ¶ ↺
      - proves proof ch:11-manifolds-tensors-curvature@proof-17 ¶
  - depends_on notation 14.1 not:lie-indices ¶
  - proves proof ch:12-lie-groups-fibre-bundles@proof-29 ¶
- depends_on proposition 14.27 Generators of $\mathfrak{so}(3)$ ¶
  - depends_on definition 14.26 The rotation group ¶ ↺
  - proves proof ch:12-lie-groups-fibre-bundles@proof-8 ¶
depends_on proposition 29.5 The velocity field of a rigid body ¶
- depends_on definition 29.4 Angular velocity ¶ ↺
- depends_on equation 29.1 eq:rigid-constraint ¶
- proves proof ch:12-rigid-body-rotating-frames@proof-3 ¶
proves proof ch:12-rigid-body-rotating-frames@proof-5 ¶

Supports

depends_on proposition 29.47 The gyrocompass ¶
depends_on theorem 29.25 Euler's equations ¶
- depends_on phenomenon 29.46 A fast spinning top does not fall ¶
  - depends_on phenomenon 29.49 Precession of the equinoxes ¶
    - depends_on proposition 29.50 The principal nutation ¶
- depends_on phenomenon 29.31 The intermediate-axis instability ¶
  - depends_on remark 29.32 What the linearization is entitled to conclude ¶
- depends_on proposition 29.26 The two integrals of torque-free motion ¶
  - depends_on proposition 29.33 Dissipation drives a free body to its largest moment ¶
  - 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 remark 29.27 Euler's equations as a Lie–Poisson system ¶
  - depends_on remark 29.30 Polhode and herpolhode ¶
  - depends_on remark 24.42 The intermediate axis ¶
  - depends_on theorem 29.29 Poinsot's construction ¶
    - depends_on remark 29.32 What the linearization is entitled to conclude ¶ ↺
    - depends_on remark 29.30 Polhode and herpolhode ¶ ↺
- depends_on proposition 29.28 Free rotation of a symmetric body ¶
  - depends_on phenomenon 29.34 Free nutation of the Earth ¶
- depends_on proposition 24.41 The free rigid body is a Lie–Poisson system ¶
  - depends_on remark 24.48 Reduction is what physicists do without saying so ¶
    - depends_on example A.573 The abelian case, and eliminating a cyclic coordinate ¶
  - depends_on remark 24.42 The intermediate axis ¶ ↺
depends_on theorem 29.51 Equation of motion in a rotating frame ¶
- depends_on phenomenon 42.4 The lunar orbit is not polarized toward the Sun ¶
  - tests experiment Lunar laser ranging and Gravity Probe B ¶
    - cites (method) derived bib 22 Gravity Probe B: Final Results of a Space Experiment to Test General Relativity ¶
    - cites (evidence) derived bib 22 Gravity Probe B: Final Results of a Space Experiment to Test General Relativity ¶ ↺
    - cites (evidence) derived bib 22 Gravity Probe B: Final Results of a Space Experiment to Test General Relativity ¶ ↺
    - cites (history) derived bib Über den Einfluß der Eigenrotation der Zentralkörper auf die Bewegung der Planeten und Monde nach der Einsteinschen Gravitationstheorie ¶
    - cites (method) derived bib 18 APOLLO: millimeter lunar laser ranging ¶
    - cites (history) derived bib 5 Equivalence Principle for Massive Bodies. II. Theory ¶
    - cites (history) derived bib 5 Equivalence Principle for Massive Bodies. II. Theory ¶ ↺
    - cites (history) derived bib Über die Wirkung rotierender ferner Massen in der Einsteinschen Gravitationstheorie ¶
    - cites (method) derived bib 26 Progress in Lunar Laser Ranging Tests of Relativistic Gravity ¶
    - cites (evidence) derived bib 26 Progress in Lunar Laser Ranging Tests of Relativistic Gravity ¶ ↺
    - cites (evidence) derived bib 26 Progress in Lunar Laser Ranging Tests of Relativistic Gravity ¶ ↺

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Edges

type	direction	node	provenance	where
`depends_on`	→	Angular velocity	declared	parts/03-classical-mechanics/12-rigid-body-rotating-frames.tex:176
`depends_on`	→	The velocity field of a rigid body	declared	parts/03-classical-mechanics/12-rigid-body-rotating-frames.tex:176
`depends_on`	←	The gyrocompass	declared	parts/03-classical-mechanics/12-rigid-body-rotating-frames.tex:1785
`depends_on`	←	Euler's equations	declared	parts/03-classical-mechanics/12-rigid-body-rotating-frames.tex:752
`depends_on`	←	Equation of motion in a rotating frame	declared	parts/03-classical-mechanics/12-rigid-body-rotating-frames.tex:2153
`proves`	←	ch:12-rigid-body-rotating-frames@proof-5	declared	parts/03-classical-mechanics/12-rigid-body-rotating-frames.tex:179