phenomenon 29.49 Precession of the equinoxes

open in the book · parts/03-classical-mechanics/12-rigid-body-rotating-frames.tex:1880 · p. 997

phenomenon-tested: no experiment declares a \tests edge to it and it is not listed in untested.txt

Rests on

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 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-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 ¶
      - depends_on definition 9.108 Rodrigues formula ¶
      - depends_on equation 9.146 eq:slt-legendre-ode ¶
      - proves proof ch:07-odes-sturm-liouville@proof-53 ¶
    - 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 ¶

Supports

depends_on proposition 29.50 The principal nutation ¶

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
`cites`	→	Philosophiæ Naturalis Principia Mathematica	derived	parts/03-classical-mechanics/12-rigid-body-rotating-frames.tex:1894
`depends_on`	→	A fast spinning top does not fall	declared	parts/03-classical-mechanics/12-rigid-body-rotating-frames.tex:1897
`depends_on`	→	MacCullagh's formula	declared	parts/03-classical-mechanics/12-rigid-body-rotating-frames.tex:1897
`depends_on`	←	The principal nutation	declared	parts/03-classical-mechanics/12-rigid-body-rotating-frames.tex:2011
`proves`	←	ch:12-rigid-body-rotating-frames@proof-32	declared	parts/03-classical-mechanics/12-rigid-body-rotating-frames.tex:1900