proposition 29.24 MacCullagh's formula

open in the book · parts/03-classical-mechanics/12-rigid-body-rotating-frames.tex:679 · p. 983

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 ¶ ↺
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 ¶

Supports

depends_on phenomenon 29.49 Precession of the equinoxes ¶
- depends_on proposition 29.50 The principal nutation ¶

Neighborhood

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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:690
`depends_on`	→	Generating function	declared	parts/03-classical-mechanics/12-rigid-body-rotating-frames.tex:690
`depends_on`	←	Precession of the equinoxes	declared	parts/03-classical-mechanics/12-rigid-body-rotating-frames.tex:1897
`proves`	←	ch:12-rigid-body-rotating-frames@proof-15	declared	parts/03-classical-mechanics/12-rigid-body-rotating-frames.tex:693