proposition 29.8 Chasles: the general displacement is a screw

open in the book · parts/03-classical-mechanics/12-rigid-body-rotating-frames.tex:203 · p. 979

Rests on

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 ¶
depends_on theorem 29.3 Euler's rotation theorem ¶
- depends_on proposition 14.30 Rodrigues formula; the exponential map is onto ¶
  - depends_on equation 14.28 eq:lie-expso2 ¶
  - depends_on equation 14.25 eq:lie-so2-matrix ¶
  - depends_on proposition 14.27 Generators of $\mathfrak{so}(3)$ ¶ ↺
  - proves proof ch:12-lie-groups-fibre-bundles@proof-9 ¶
- depends_on proposition 29.2 Six degrees of freedom ¶
  - depends_on definition 21.9 Degrees of freedom ¶
  - depends_on definition 29.1 Rigid body ¶
    - depends_on definition 21.2 Holonomic constraint ¶
    - depends_on definition 19.39 Body ¶
      - depends_on definition 18.4 Body ¶
      - depends_on definition 19.3 Mass ¶
  - proves proof ch:12-rigid-body-rotating-frames@proof-1 ¶
- proves proof ch:12-rigid-body-rotating-frames@proof-2 ¶
proves proof ch:12-rigid-body-rotating-frames@proof-6 ¶

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type	direction	node	provenance	where
`cites`	→	Note sur les propriétés générales du système de deux corps semblables entr'eux et placés d'une manière quelconque dans l'espace; et sur le déplacement fini ou infiniment petit d'un corps solide libre	derived	parts/03-classical-mechanics/12-rigid-body-rotating-frames.tex:207
`depends_on`	→	The velocity field of a rigid body	declared	parts/03-classical-mechanics/12-rigid-body-rotating-frames.tex:208
`depends_on`	→	Euler's rotation theorem	declared	parts/03-classical-mechanics/12-rigid-body-rotating-frames.tex:208
`proves`	←	ch:12-rigid-body-rotating-frames@proof-6	declared	parts/03-classical-mechanics/12-rigid-body-rotating-frames.tex:211