definition 14.26 The rotation group

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Supports

• depends_on definition A.672 The octahedral rotation group ¶
  • depends_on proposition A.673 Cubic tensors of rank four ¶
    • depends_on theorem A.675 Three constants for a cubic crystal, two for an isotropic solid ¶
      • depends_on remark A.676 The third cubic constant is measured, and it is not small ¶
• depends_on definition 29.4 Angular velocity ¶
  • depends_on proposition 29.11 Angular velocity in Euler angles ¶
    • depends_on definition 29.35 The Lagrange top ¶
    • depends_on remark 29.12 The coordinate singularity, and what it is not ¶
  • depends_on proposition 29.5 The velocity field of a rigid body ¶
    • depends_on proposition 29.14 Angular momentum and kinetic energy ¶
    • depends_on proposition 29.8 Chasles: the general displacement is a screw ¶
    • depends_on proposition 29.6 The angular velocity does not depend on the base point ¶
    • depends_on theorem 29.7 Transport theorem ¶
      • depends_on proposition 29.47 The gyrocompass ¶
      • depends_on theorem 29.25 Euler's equations ¶
        • depends_on phenomenon 29.46 A fast spinning top does not fall ¶
        • depends_on phenomenon 29.31 The intermediate-axis instability ¶
        • depends_on proposition 29.26 The two integrals of torque-free motion ¶
        • depends_on proposition 29.28 Free rotation of a symmetric body ¶
        • depends_on proposition 24.41 The free rigid body is a Lie–Poisson system ¶
      • depends_on theorem 29.51 Equation of motion in a rotating frame ¶
        • depends_on phenomenon 42.4 The lunar orbit is not polarized toward the Sun ¶
  • depends_on theorem 29.7 Transport theorem ¶ ↺
• depends_on lemma A.742 Isotropic representation ¶
  • depends_on corollary A.743 Two scalar functions instead of a tensor field ¶
    • depends_on lemma A.748 The second-order structure function ¶
      • depends_on theorem A.749 Kolmogorov's equation and the four-fifths law ¶
    • depends_on lemma A.747 The third-order structure functions ¶
      • depends_on theorem A.749 Kolmogorov's equation and the four-fifths law ¶ ↺
    • depends_on proposition A.746 The Kármán–Howarth equation in classical form ¶
  • depends_on lemma A.747 The third-order structure functions ¶ ↺
  • depends_on lemma A.744 Vanishing of the pressure–velocity correlation ¶
    • depends_on theorem A.745 Kármán–Howarth–Monin relation ¶
      • depends_on proposition A.746 The Kármán–Howarth equation in classical form ¶ ↺
      • depends_on theorem A.749 Kolmogorov's equation and the four-fifths law ¶ ↺
• depends_on notation 29.9 The $z$–$x$–$z$ Euler angles used in this treatise ¶
  • depends_on proposition 29.11 Angular velocity in Euler angles ¶ ↺
  • depends_on remark 29.10 Other conventions, and why the choice must be stated ¶
• depends_on proposition 14.27 Generators of $\mathfrak{so}(3)$ ¶
  • depends_on definition 14.28 Hermitian rotation generators ¶
  • depends_on definition 29.4 Angular velocity ¶ ↺
  • depends_on proposition 14.30 Rodrigues formula; the exponential map is onto ¶
    • depends_on proposition 14.31 $\SO(3,\R)$ is not simply connected ¶
      • depends_on remark 29.12 The coordinate singularity, and what it is not ¶ ↺
    • depends_on theorem 14.37 $\SU(2)$ is a two-to-one cover of $\SO(3,\R)$ ¶
      • depends_on corollary 14.38 $\SU(2)$ is the universal cover ¶
        • depends_on proposition 14.31 $\SO(3,\R)$ is not simply connected ¶ ↺
        • depends_on proposition 14.45 Which representations descend to $\SO(3,\R)$ ¶
      • depends_on lemma A.369 $\Phi$ is a two-sheeted covering ¶
    • depends_on theorem 29.3 Euler's rotation theorem ¶
      • depends_on notation 29.9 The $z$–$x$–$z$ Euler angles used in this treatise ¶ ↺
      • depends_on proposition 125.2 Crystallographic restriction ¶
        • depends_on remark 125.3 What the theorem does and does not forbid ¶
      • depends_on proposition 29.8 Chasles: the general displacement is a screw ¶ ↺
  • depends_on remark 18.30 The angular velocity is an element of $\mathfrak{so}(3)$ ¶