theorem 29.3 Euler's rotation theorem

open in the book · parts/03-classical-mechanics/12-rigid-body-rotating-frames.tex:77 · p. 978

Rests on

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 $\mathfrak{so}(3)$ ¶
  - depends_on definition 14.26 The rotation group ¶
  - proves proof ch:12-lie-groups-fibre-bundles@proof-8 ¶
- 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 18.3 Particle ¶
    - depends_on definition 19.3 Mass ¶
      - depends_on definition 18.3 Particle ¶ ↺
      - depends_on postulate 19.1 Inertia ¶
- proves proof ch:12-rigid-body-rotating-frames@proof-1 ¶
proves proof ch:12-rigid-body-rotating-frames@proof-2 ¶

Supports

depends_on notation 29.9 The $z$–$x$–$z$ Euler angles used in this treatise ¶
- 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 remark 29.10 Other conventions, and why the choice must be stated ¶
depends_on proposition 125.2 Crystallographic restriction ¶
- depends_on remark 125.3 What the theorem does and does not forbid ¶
depends_on proposition 29.8 Chasles: the general displacement is a screw ¶

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`	→	Rodrigues formula; the exponential map is onto	declared	parts/03-classical-mechanics/12-rigid-body-rotating-frames.tex:82
`depends_on`	→	Six degrees of freedom	declared	parts/03-classical-mechanics/12-rigid-body-rotating-frames.tex:82
`depends_on`	←	The $z$–$x$–$z$ Euler angles used in this treatise	declared	parts/03-classical-mechanics/12-rigid-body-rotating-frames.tex:265
`depends_on`	←	Crystallographic restriction	declared	parts/12-statistical-mechanics/08-phonons-lattices.tex:127
`depends_on`	←	Chasles: the general displacement is a screw	declared	parts/03-classical-mechanics/12-rigid-body-rotating-frames.tex:208
`proves`	←	ch:12-rigid-body-rotating-frames@proof-2	declared	parts/03-classical-mechanics/12-rigid-body-rotating-frames.tex:85