definition 29.4 Angular velocity

open in the book · parts/03-classical-mechanics/12-rigid-body-rotating-frames.tex:100 · p. 978

ground object -- no derivation owed

Rests on

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 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 ¶

Supports

depends_on proposition 29.11 Angular velocity in Euler angles ¶
- depends_on definition 29.35 The Lagrange top ¶
- depends_on remark 29.12 The coordinate singularity, and what it is not ¶
depends_on proposition 29.5 The velocity field of a rigid body ¶
- depends_on proposition 29.14 Angular momentum and kinetic energy ¶
- depends_on proposition 29.8 Chasles: the general displacement is a screw ¶
- depends_on proposition 29.6 The angular velocity does not depend on the base point ¶
- depends_on theorem 29.7 Transport theorem ¶
  - 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 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 29.27 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 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 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 ¶
depends_on theorem 29.7 Transport theorem ¶ ↺

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`	→	The rotation group	declared	parts/03-classical-mechanics/12-rigid-body-rotating-frames.tex:114
`depends_on`	→	The Levi-Civita symbol is invariant	declared	parts/03-classical-mechanics/12-rigid-body-rotating-frames.tex:114
`depends_on`	→	Generators of $\mathfrak{so}(3)$	declared	parts/03-classical-mechanics/12-rigid-body-rotating-frames.tex:114
`depends_on`	←	Angular velocity in Euler angles	declared	parts/03-classical-mechanics/12-rigid-body-rotating-frames.tex:295
`depends_on`	←	The velocity field of a rigid body	declared	parts/03-classical-mechanics/12-rigid-body-rotating-frames.tex:131
`depends_on`	←	Transport theorem	declared	parts/03-classical-mechanics/12-rigid-body-rotating-frames.tex:176