proposition 29.14 Angular momentum and kinetic energy

open in the book · parts/03-classical-mechanics/12-rigid-body-rotating-frames.tex:377 · p. 981

Rests on

depends_on definition 19.55 Angular momentum of the centre of mass ¶
- depends_on definition 19.18 Angular momentum ¶
  - depends_on definition 18.3 Particle ¶
  - 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 18.9 Position ¶
      - depends_on definition 13.9 Tangent vector to a curve ¶
    - depends_on definition 19.3 Mass ¶
      - depends_on definition 18.3 Particle ¶ ↺
      - depends_on postulate 19.1 Inertia ¶
- depends_on definition 19.51 Linear momentum of the centre of mass ¶
  - depends_on definition 19.47 Position of the centre of mass ¶
    - depends_on definition 19.39 Body ¶
      - depends_on definition 18.4 Body ¶
      - depends_on definition 19.3 Mass ¶ ↺
    - depends_on definition 19.40 Total mass ¶
      - depends_on definition 19.39 Body ¶ ↺
      - depends_on definition 19.3 Mass ¶ ↺
  - depends_on definition 19.5 Linear momentum ¶ ↺
depends_on definition 29.13 Inertia tensor, continuum form ¶
- depends_on definition 7.125 Multiple integral ¶
  - depends_on axiom 7.1 Completeness of $\R$ ¶
  - depends_on definition 7.39 Darboux sums and the definite integral ¶
    - depends_on axiom 7.1 Completeness of $\R$ ¶ ↺
- depends_on definition 13.5 Tensor under orthogonal transformations ¶
  - depends_on definition 13.4 Orthogonal coordinate transformation ¶
    - depends_on definition 13.3 Orthogonal coordinate system ¶
- depends_on definition 19.42 Inertia tensor ¶
  - depends_on definition 13.5 Tensor under orthogonal transformations ¶ ↺
  - depends_on definition 19.41 Moment of inertia about an axis ¶
    - depends_on definition 19.39 Body ¶ ↺
    - depends_on definition 19.3 Mass ¶ ↺
depends_on proposition 29.5 The velocity field of a rigid body ¶
- 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 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-8 ¶

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type	direction	node	provenance	where
`depends_on`	→	Angular momentum of the centre of mass	declared	parts/03-classical-mechanics/12-rigid-body-rotating-frames.tex:392
`depends_on`	→	Inertia tensor, continuum form	declared	parts/03-classical-mechanics/12-rigid-body-rotating-frames.tex:392
`depends_on`	→	The velocity field of a rigid body	declared	parts/03-classical-mechanics/12-rigid-body-rotating-frames.tex:392
`proves`	←	ch:12-rigid-body-rotating-frames@proof-8	declared	parts/03-classical-mechanics/12-rigid-body-rotating-frames.tex:396