proposition 29.47 The gyrocompass

open in the book · parts/03-classical-mechanics/12-rigid-body-rotating-frames.tex:1772 · p. 996

Rests on

depends_on equation 29.11 eq:rigid-angular-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-31 ¶

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type	direction	node	provenance	where
`cites`	→	Classical Mechanics	derived	parts/03-classical-mechanics/12-rigid-body-rotating-frames.tex:1784
`depends_on`	→	eq:rigid-angular-momentum	declared	parts/03-classical-mechanics/12-rigid-body-rotating-frames.tex:1785
`depends_on`	→	Transport theorem	declared	parts/03-classical-mechanics/12-rigid-body-rotating-frames.tex:1785
`proves`	←	ch:12-rigid-body-rotating-frames@proof-31	declared	parts/03-classical-mechanics/12-rigid-body-rotating-frames.tex:1788