proposition 29.2 Six degrees of freedom

open in the book · parts/03-classical-mechanics/12-rigid-body-rotating-frames.tex:54 · p. 977

Rests on

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 ¶
      - depends_on definition 18.8 Inertial frame of reference ¶
      - depends_on definition 18.3 Particle ¶ ↺
proves proof ch:12-rigid-body-rotating-frames@proof-1 ¶

Supports

depends_on theorem 29.3 Euler's rotation theorem ¶
- 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`	→	Degrees of freedom	declared	parts/03-classical-mechanics/12-rigid-body-rotating-frames.tex:59
`depends_on`	→	Rigid body	declared	parts/03-classical-mechanics/12-rigid-body-rotating-frames.tex:59
`depends_on`	←	Euler's rotation theorem	declared	parts/03-classical-mechanics/12-rigid-body-rotating-frames.tex:82
`proves`	←	ch:12-rigid-body-rotating-frames@proof-1	declared	parts/03-classical-mechanics/12-rigid-body-rotating-frames.tex:62