proposition 29.33 Dissipation drives a free body to its largest moment

open in the book · parts/03-classical-mechanics/12-rigid-body-rotating-frames.tex:1050 · p. 988

Rests on

depends_on proposition 29.26 The two integrals of torque-free motion ¶
- depends_on equation 29.12 eq:rigid-kinetic-energy ¶
- depends_on theorem 29.25 Euler's equations ¶
  - depends_on postulate 19.22 Newton's second law, rotational case ¶
    - depends_on definition 19.18 Angular momentum ¶
      - depends_on definition 18.3 Particle ¶
      - depends_on definition 19.5 Linear momentum ¶
    - depends_on postulate 19.8 Newton's second law ¶
      - depends_on definition 19.5 Linear momentum ¶ ↺
      - depends_on postulate 19.6 Newton's first law ¶
  - depends_on theorem 29.16 Principal axes ¶
    - depends_on definition 29.13 Inertia tensor, continuum form ¶
      - depends_on definition 7.125 Multiple integral ¶
      - depends_on definition 13.5 Tensor under orthogonal transformations ¶
      - depends_on definition 19.42 Inertia tensor ¶
    - depends_on proposition 29.15 Positivity ¶
      - depends_on definition 29.13 Inertia tensor, continuum form ¶ ↺
      - proves proof ch:12-rigid-body-rotating-frames@proof-9 ¶
    - depends_on theorem 5.79 Spectral theorem for a self-adjoint operator ¶
      - depends_on corollary 5.72 Existence of an eigenvalue over $\C$ ¶
      - depends_on definition 5.41 Adjoint ¶
      - depends_on theorem 5.40 Rank–nullity ¶
      - proves proof ch:03-linear-algebra-representations@proof-31 ¶
    - proves proof ch:12-rigid-body-rotating-frames@proof-10 ¶
  - depends_on theorem 29.7 Transport theorem ¶
    - depends_on definition 29.4 Angular velocity ¶
      - depends_on definition 14.26 The rotation group ¶
      - depends_on lemma 14.62 The Levi-Civita symbol is invariant ¶
      - depends_on proposition 14.27 Generators of $\mathfrak{so}(3)$ ¶
    - depends_on proposition 29.5 The velocity field of a rigid body ¶
      - depends_on definition 29.4 Angular velocity ¶ ↺
      - depends_on equation 29.1 eq:rigid-constraint ¶
      - proves proof ch:12-rigid-body-rotating-frames@proof-3 ¶
    - proves proof ch:12-rigid-body-rotating-frames@proof-5 ¶
  - proves proof ch:12-rigid-body-rotating-frames@proof-16 ¶
- proves proof ch:12-rigid-body-rotating-frames@proof-17 ¶
depends_on theorem 29.16 Principal axes ¶ ↺
proves proof ch:12-rigid-body-rotating-frames@proof-21 ¶

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type	direction	node	provenance	where
`depends_on`	→	The two integrals of torque-free motion	declared	parts/03-classical-mechanics/12-rigid-body-rotating-frames.tex:1062
`depends_on`	→	Principal axes	declared	parts/03-classical-mechanics/12-rigid-body-rotating-frames.tex:1062
`proves`	←	ch:12-rigid-body-rotating-frames@proof-21	declared	parts/03-classical-mechanics/12-rigid-body-rotating-frames.tex:1065