notation 29.9 The $z$–$x$–$z$ Euler angles used in this treatise

open in the book · parts/03-classical-mechanics/12-rigid-body-rotating-frames.tex:230 · p. 979

notation -- no derivation owed by its kind

Rests on

depends_on definition 14.26 The rotation group ¶
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 $\mathfrak{so}(3)$ ¶
    - 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 19.3 Mass ¶
  - proves proof ch:12-rigid-body-rotating-frames@proof-1 ¶
- proves proof ch:12-rigid-body-rotating-frames@proof-2 ¶

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 remark 29.10 Other conventions, and why the choice must be stated ¶

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:265
`depends_on`	→	Euler's rotation theorem	declared	parts/03-classical-mechanics/12-rigid-body-rotating-frames.tex:265
`depends_on`	←	Angular velocity in Euler angles	declared	parts/03-classical-mechanics/12-rigid-body-rotating-frames.tex:295
`depends_on`	←	Other conventions, and why the choice must be stated	declared	parts/03-classical-mechanics/12-rigid-body-rotating-frames.tex:280