theorem 29.51 Equation of motion in a rotating frame

open in the book · parts/03-classical-mechanics/12-rigid-body-rotating-frames.tex:2137 · p. 1000

Rests on

depends_on postulate 19.8 Newton's second law ¶
- depends_on definition 19.5 Linear momentum ¶
  - depends_on definition 18.10 Velocity ¶
    - depends_on definition 7.26 Derivative of a function at a point ¶
      - depends_on definition 7.16 Limit ¶
      - depends_on definition 7.9 Real function ¶
    - depends_on definition 18.9 Position ¶
      - depends_on definition 18.7 Frame of reference ¶
      - depends_on definition 18.3 Particle ¶
    - depends_on definition 13.9 Tangent vector to a curve ¶
      - depends_on definition 13.8 Curve ¶
  - depends_on definition 19.3 Mass ¶
    - depends_on definition 18.3 Particle ¶ ↺
    - depends_on postulate 19.1 Inertia ¶
      - depends_on definition 18.8 Inertial frame of reference ¶
      - depends_on definition 18.3 Particle ¶ ↺
- depends_on postulate 19.6 Newton's first law ¶
  - depends_on definition 18.8 Inertial frame of reference ¶ ↺
  - depends_on definition 19.5 Linear momentum ¶ ↺
depends_on theorem 29.7 Transport theorem ¶
- 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 proposition 13.93 Algebra of densities ¶
    - 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 ¶
proves proof ch:12-rigid-body-rotating-frames@proof-34 ¶

Supports

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
`cites`	→	Sur les équations du mouvement relatif des systèmes de corps	derived	parts/03-classical-mechanics/12-rigid-body-rotating-frames.tex:2151
`cites`	→	Horologium Oscillatorium sive de motu pendulorum ad horologia aptato demonstrationes geometricae	derived	parts/03-classical-mechanics/12-rigid-body-rotating-frames.tex:2152
`depends_on`	→	Newton's second law	declared	parts/03-classical-mechanics/12-rigid-body-rotating-frames.tex:2153
`depends_on`	→	Transport theorem	declared	parts/03-classical-mechanics/12-rigid-body-rotating-frames.tex:2153
`depends_on`	←	The lunar orbit is not polarized toward the Sun	declared	parts/05-general-relativity-cosmology/01-equivalence-classical-tests.tex:327
`proves`	←	ch:12-rigid-body-rotating-frames@proof-34	declared	parts/03-classical-mechanics/12-rigid-body-rotating-frames.tex:2156