theorem 29.20 Parallel-axis theorem

open in the book · parts/03-classical-mechanics/12-rigid-body-rotating-frames.tex:548 · p. 982

Rests on

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 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 ¶ ↺
- depends_on definition 19.40 Total mass ¶
  - depends_on definition 19.39 Body ¶ ↺
  - depends_on definition 19.3 Mass ¶ ↺
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 ¶ ↺
proves proof ch:12-rigid-body-rotating-frames@proof-12 ¶

Supports

depends_on corollary 29.21 The centre of mass minimizes the moment ¶

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`	→	Position of the centre of mass	declared	parts/03-classical-mechanics/12-rigid-body-rotating-frames.tex:559
`depends_on`	→	Inertia tensor, continuum form	declared	parts/03-classical-mechanics/12-rigid-body-rotating-frames.tex:559
`depends_on`	←	The centre of mass minimizes the moment	declared	parts/03-classical-mechanics/12-rigid-body-rotating-frames.tex:587
`proves`	←	ch:12-rigid-body-rotating-frames@proof-12	declared	parts/03-classical-mechanics/12-rigid-body-rotating-frames.tex:562