definition 19.42 Inertia tensor

open in the book · parts/03-classical-mechanics/02-newtonian-dynamics.tex:1230 · p. 748

ground object -- no derivation owed

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 19.41 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 18.8 Inertial frame of reference ¶
      - depends_on definition 18.3 Particle ¶ ↺
- depends_on definition 19.3 Mass ¶ ↺

Supports

depends_on definition 29.13 Inertia tensor, continuum form ¶
- depends_on definition 29.19 Inertia ellipsoid ¶
  - depends_on theorem 29.29 Poinsot's construction ¶
    - depends_on remark 29.32 What the linearization is entitled to conclude ¶
    - depends_on remark 29.30 Polhode and herpolhode ¶
- depends_on example 29.23 The polar moment of the Earth, and what it reveals ¶
  - depends_on phenomenon 29.34 Free nutation of the Earth ¶
- depends_on proposition 49.17 Magnetic-dipole spin-down ¶
- depends_on proposition 29.14 Angular momentum and kinetic energy ¶
- depends_on proposition 29.15 Positivity ¶
  - depends_on definition 29.19 Inertia ellipsoid ¶ ↺
  - depends_on theorem 29.16 Principal axes ¶
    - depends_on definition 29.19 Inertia ellipsoid ¶ ↺
    - depends_on definition 29.35 The Lagrange top ¶
    - depends_on definition 29.18 Classification of tops ¶
      - depends_on proposition 29.28 Free rotation of a symmetric body ¶
    - depends_on phenomenon 29.31 The intermediate-axis instability ¶
      - depends_on remark 29.32 What the linearization is entitled to conclude ¶ ↺
    - depends_on proposition 29.33 Dissipation drives a free body to its largest moment ¶
    - depends_on proposition 29.17 Triangle inequalities ¶
      - depends_on proposition 29.22 Perpendicular-axis theorem ¶
    - depends_on theorem 29.25 Euler's equations ¶
      - depends_on phenomenon 29.46 A fast spinning top does not fall ¶
      - depends_on phenomenon 29.31 The intermediate-axis instability ¶ ↺
      - depends_on proposition 29.26 The two integrals of torque-free motion ¶
      - depends_on proposition 29.28 Free rotation of a symmetric body ¶ ↺
      - depends_on proposition 24.41 The free rigid body is a Lie–Poisson system ¶
- depends_on proposition 29.24 MacCullagh's formula ¶
  - depends_on phenomenon 29.49 Precession of the equinoxes ¶
    - depends_on proposition 29.50 The principal nutation ¶
- depends_on proposition 29.22 Perpendicular-axis theorem ¶ ↺
- depends_on theorem 29.20 Parallel-axis theorem ¶
  - depends_on corollary 29.21 The centre of mass minimizes the moment ¶
- depends_on theorem 29.16 Principal axes ¶ ↺
depends_on example 19.45 The uniform solid sphere ¶
depends_on proposition 19.43 The moment of inertia is a quadratic form in the axis ¶

Neighborhood

Every logical edge within two steps of this node.

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partly declared
a check failed
not graded
declared in the source
inferred from structure

Edges

type	direction	node	provenance	where
`depends_on`	→	Tensor under orthogonal transformations	declared	parts/03-classical-mechanics/02-newtonian-dynamics.tex:1239
`depends_on`	→	Moment of inertia about an axis	declared	parts/03-classical-mechanics/02-newtonian-dynamics.tex:1239
`depends_on`	←	Inertia tensor, continuum form	declared	parts/03-classical-mechanics/12-rigid-body-rotating-frames.tex:373
`depends_on`	←	The uniform solid sphere	declared	parts/03-classical-mechanics/02-newtonian-dynamics.tex:1341
`depends_on`	←	The moment of inertia is a quadratic form in the axis	declared	parts/03-classical-mechanics/02-newtonian-dynamics.tex:1252