proposition 19.43 The moment of inertia is a quadratic form in the axis

open in the book · parts/03-classical-mechanics/02-newtonian-dynamics.tex:1242 · p. 748

Rests on

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 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 19.3 Mass ¶ ↺
proves proof ch:02-newtonian-dynamics@proof-13 ¶

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Every logical edge within two steps of this node.

type	direction	node	provenance	where
`depends_on`	→	Tensor under orthogonal transformations	declared	parts/03-classical-mechanics/02-newtonian-dynamics.tex:1252
`depends_on`	→	Inertia tensor	declared	parts/03-classical-mechanics/02-newtonian-dynamics.tex:1252
`proves`	←	ch:02-newtonian-dynamics@proof-13	declared	parts/03-classical-mechanics/02-newtonian-dynamics.tex:1255