remark 29.44 The Kovalevskaya integral

open in the book · parts/03-classical-mechanics/12-rigid-body-rotating-frames.tex:1606 · p. 994

remark -- no derivation owed by its kind

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depends_on proposition 29.43 The three integrable heavy tops ¶
- 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 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-17 ¶
- depends_on proposition 29.36 Three first integrals ¶
  - depends_on equation 29.35 eq:rigid-top-lagrangian ¶
  - depends_on theorem 21.36 Conservation of the conjugate momentum ¶
    - depends_on definition 21.35 Cyclic coordinate ¶
    - depends_on equation 21.39 eq:lag-el-conservative ¶
    - depends_on equation 21.43 eq:lag-generalized-momentum ¶
    - proves proof ch:04-lagrangian-mechanics@proof-8 ¶
  - depends_on theorem 21.43 Conservation of energy ¶
    - depends_on equation 21.51 eq:lag-energy-dot-cons ¶
    - depends_on equation 21.46 eq:lag-energy-h ¶
    - depends_on theorem 19.32 Conservation of energy ¶
      - depends_on definition 19.31 Energy ¶
      - depends_on equation 19.19 eq:newt-conservative ¶
      - depends_on equation 19.4 eq:newt-fma ¶
      - proves proof ch:02-newtonian-dynamics@proof-9 ¶
    - proves proof ch:04-lagrangian-mechanics@proof-11 ¶
  - proves proof ch:12-rigid-body-rotating-frames@proof-23 ¶
- proves proof ch:12-rigid-body-rotating-frames@proof-28 ¶

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type	direction	node	provenance	where
`depends_on`	→	The three integrable heavy tops	declared	parts/03-classical-mechanics/12-rigid-body-rotating-frames.tex:1620