proposition 29.50 The principal nutation

open in the book · parts/03-classical-mechanics/12-rigid-body-rotating-frames.tex:1990 · p. 998

Rests on

depends_on equation 29.60 eq:rigid-precession-lunisolar ¶
depends_on equation 29.57 eq:rigid-quadrupole-energy ¶
depends_on phenomenon 29.49 Precession of the equinoxes ¶
- depends_on phenomenon 29.46 A fast spinning top does not fall ¶
  - depends_on equation 19.14 eq:newt-torque ¶
  - 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 postulate 19.8 Newton's second law ¶
    - depends_on theorem 29.16 Principal axes ¶
      - depends_on definition 29.13 Inertia tensor, continuum form ¶
      - depends_on proposition 29.15 Positivity ¶
      - depends_on theorem 5.79 Spectral theorem for a self-adjoint operator ¶
      - 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 proposition 29.5 The velocity field of a rigid body ¶
      - 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-30 ¶
- depends_on proposition 29.24 MacCullagh's formula ¶
  - depends_on definition 29.13 Inertia tensor, continuum form ¶ ↺
  - depends_on theorem 9.113 Generating function ¶
    - depends_on lemma 9.110 The polynomial solution is unique up to scale ¶
      - depends_on proposition 9.109 Rodrigues' polynomials solve the equation ¶
      - proves proof ch:07-odes-sturm-liouville@proof-54 ¶
    - depends_on proposition 9.109 Rodrigues' polynomials solve the equation ¶ ↺
    - proves proof ch:07-odes-sturm-liouville@proof-56 ¶
  - proves proof ch:12-rigid-body-rotating-frames@proof-15 ¶
- proves proof ch:12-rigid-body-rotating-frames@proof-32 ¶
proves proof ch:12-rigid-body-rotating-frames@proof-33 ¶

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type	direction	node	provenance	where
`depends_on`	→	eq:rigid-precession-lunisolar	declared	parts/03-classical-mechanics/12-rigid-body-rotating-frames.tex:2011
`depends_on`	→	eq:rigid-quadrupole-energy	declared	parts/03-classical-mechanics/12-rigid-body-rotating-frames.tex:2011
`depends_on`	→	Precession of the equinoxes	declared	parts/03-classical-mechanics/12-rigid-body-rotating-frames.tex:2011
`proves`	←	ch:12-rigid-body-rotating-frames@proof-33	declared	parts/03-classical-mechanics/12-rigid-body-rotating-frames.tex:2015