proposition 29.39 Steady precession

open in the book · parts/03-classical-mechanics/12-rigid-body-rotating-frames.tex:1416 · p. 992

Rests on

depends_on equation 29.35 eq:rigid-top-lagrangian ¶
depends_on theorem 16.22 Euler–Lagrange ¶
- depends_on equation 16.15 eq:calcvar-first-variation ¶
- depends_on lemma 16.20 Mixed form ¶
  - depends_on corollary 7.44 Substitution and integration by parts ¶
    - depends_on proposition 7.31 Chain rule ¶
      - depends_on definition 7.13 Composite function ¶
      - depends_on proposition 7.27 Differentiable implies continuous ¶
      - depends_on proposition 7.6 Algebra of limits ¶
      - proves proof ch:05-real-analysis@proof-15 ¶
    - depends_on proposition 7.30 Leibniz rule ¶
      - depends_on definition 7.12 Product of functions ¶
      - depends_on equation 7.14 eq:ana-derivh ¶
      - depends_on proposition 7.27 Differentiable implies continuous ¶ ↺
      - depends_on proposition 7.6 Algebra of limits ¶ ↺
      - proves proof ch:05-real-analysis@proof-14 ¶
    - depends_on theorem 7.43 Fundamental theorem of calculus, II ¶
      - depends_on definition 7.41 Antiderivative ¶
      - depends_on theorem 7.42 Fundamental theorem of calculus, I ¶
      - proves proof ch:05-real-analysis@proof-25 ¶
    - proves proof ch:05-real-analysis@proof-26 ¶
  - depends_on lemma 16.19 du Bois-Reymond ¶
    - depends_on equation 16.18 eq:calcvar-dbr-hyp ¶
    - depends_on theorem 7.42 Fundamental theorem of calculus, I ¶ ↺
    - proves proof ch:14-calculus-of-variations@proof-9 ¶
  - proves proof ch:14-calculus-of-variations@proof-10 ¶
- depends_on proposition 16.16 Stationarity is necessary ¶
  - depends_on definition 16.15 Variation; the first variation ¶
    - depends_on definition 16.11 Admissible class; functional ¶
      - depends_on definition 7.98 Functions of class $C^{1}$ ¶
      - depends_on theorem 7.40 Continuous functions are integrable ¶
    - depends_on equation 7.177 eq:ana-functional-derivative ¶
  - depends_on definition 16.13 Weak and strong extrema ¶
    - depends_on definition 16.12 The two norms; weak and strong neighbourhoods ¶
      - depends_on definition 16.11 Admissible class; functional ¶ ↺
      - depends_on definition 6.24 Metric ¶
  - depends_on lemma 7.33 Fermat: interior extremum ¶
    - depends_on definition 7.26 Derivative of a function at a point ¶
      - depends_on definition 7.16 Limit ¶
      - depends_on definition 7.9 Real function ¶
    - depends_on proposition 7.18 Two-sided limit from one-sided limits ¶
      - depends_on definition 7.16 Limit ¶ ↺
      - depends_on equation 7.7 eq:ana-limit-left ¶
      - depends_on equation 7.5 eq:ana-limit-right ¶
      - proves proof ch:05-real-analysis@proof-6 ¶
    - proves proof ch:05-real-analysis@proof-17 ¶
  - proves proof ch:14-calculus-of-variations@proof-6 ¶
- proves proof ch:14-calculus-of-variations@proof-11 ¶
proves proof ch:12-rigid-body-rotating-frames@proof-26 ¶

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type	direction	node	provenance	where
`depends_on`	→	eq:rigid-top-lagrangian	declared	parts/03-classical-mechanics/12-rigid-body-rotating-frames.tex:1430
`depends_on`	→	Euler–Lagrange	declared	parts/03-classical-mechanics/12-rigid-body-rotating-frames.tex:1430
`proves`	←	ch:12-rigid-body-rotating-frames@proof-26	declared	parts/03-classical-mechanics/12-rigid-body-rotating-frames.tex:1433