remark 29.30 Polhode and herpolhode

Rests on

• 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 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-17 ¶
• depends_on theorem 29.29 Poinsot's construction ¶
  • depends_on definition 29.19 Inertia ellipsoid ¶
    • depends_on definition 29.13 Inertia tensor, continuum form ¶ ↺
    • depends_on proposition 29.15 Positivity ¶ ↺
    • depends_on theorem 29.16 Principal axes ¶ ↺
  • depends_on proposition 29.26 The two integrals of torque-free motion ¶ ↺
  • proves proof ch:12-rigid-body-rotating-frames@proof-19 ¶

Supports

Nothing declares a dependency on this node yet.