proposition 29.15 Positivity

open in the book · parts/03-classical-mechanics/12-rigid-body-rotating-frames.tex:431 · p. 981

Rests on

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 18.4 Body ¶
      - depends_on definition 19.3 Mass ¶
    - depends_on definition 19.3 Mass ¶ ↺
proves proof ch:12-rigid-body-rotating-frames@proof-9 ¶

Supports

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 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 29.34 Free nutation of the Earth ¶
- 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 29.49 Precession of the equinoxes ¶
      - depends_on proposition 29.50 The principal nutation ¶
  - depends_on phenomenon 29.31 The intermediate-axis instability ¶ ↺
  - depends_on proposition 29.26 The two integrals of torque-free motion ¶
    - depends_on proposition 29.33 Dissipation drives a free body to its largest moment ¶ ↺
    - depends_on proposition 29.43 The three integrable heavy tops ¶
      - depends_on remark 29.45 What integrability buys, and where it stops ¶
      - depends_on remark 29.44 The Kovalevskaya integral ¶
    - depends_on remark 29.27 Euler's equations as a Lie–Poisson system ¶
    - depends_on remark 29.30 Polhode and herpolhode ¶ ↺
    - depends_on remark 24.42 The intermediate axis ¶
    - depends_on theorem 29.29 Poinsot's construction ¶ ↺
  - 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 remark 24.48 Reduction is what physicists do without saying so ¶
      - depends_on example A.573 The abelian case, and eliminating a cyclic coordinate ¶
    - depends_on remark 24.42 The intermediate axis ¶ ↺

Neighborhood

Every logical edge within two steps of this node.

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partly declared
a check failed
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Edges

type	direction	node	provenance	where
`depends_on`	→	Inertia tensor, continuum form	declared	parts/03-classical-mechanics/12-rigid-body-rotating-frames.tex:441
`depends_on`	←	Inertia ellipsoid	declared	parts/03-classical-mechanics/12-rigid-body-rotating-frames.tex:535
`depends_on`	←	Principal axes	declared	parts/03-classical-mechanics/12-rigid-body-rotating-frames.tex:466
`proves`	←	ch:12-rigid-body-rotating-frames@proof-9	declared	parts/03-classical-mechanics/12-rigid-body-rotating-frames.tex:444