definition 13.91 Symmetric and antisymmetric parts

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• depends_on definition 30.6 Linear strain and infinitesimal rotation ¶
  • depends_on definition A.680 Kirchhoff kinematics ¶
    • depends_on lemma A.687 Kinetic energy ¶
      • depends_on theorem A.688 The Kirchhoff plate equation ¶
        • depends_on remark A.690 Poisson's count, and why it cannot be right ¶
        • depends_on theorem A.691 Kirchhoff's edge conditions and the corner force ¶
    • depends_on lemma A.681 Strains under the Kirchhoff hypothesis ¶
      • depends_on proposition A.684 The plate energy ¶
        • depends_on lemma A.685 The Gaussian-curvature term is a null Lagrangian ¶
        • depends_on theorem A.688 The Kirchhoff plate equation ¶ ↺
  • depends_on definition 30.24 The elasticity tensor ¶
    • depends_on definition 30.37 Voigt notation ¶
      • depends_on remark 30.39 The rari-constant controversy, decided by measurement ¶
    • depends_on phenomenon 30.28 Hooke's law ¶
      • depends_on phenomenon 30.32 Poisson contraction ¶
        • depends_on proposition 30.33 Conversion among the moduli ¶
      • depends_on remark 30.78 Anharmonicity: what the quadratic energy also suppresses ¶
    • depends_on proposition 30.25 Twenty-one constants ¶
      • depends_on definition 30.37 Voigt notation ¶ ↺
      • depends_on proposition 30.38 The Cauchy relations ¶
        • depends_on remark 30.39 The rari-constant controversy, decided by measurement ¶ ↺
      • 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 proposition 30.38 The Cauchy relations ¶ ↺
    • depends_on remark 30.78 Anharmonicity: what the quadratic energy also suppresses ¶ ↺
    • depends_on theorem A.675 Three constants for a cubic crystal, two for an isotropic solid ¶ ↺
  • depends_on definition 30.11 Green strain ¶
    • depends_on proposition 30.12 The Green strain measures length exactly ¶
      • depends_on example 30.13 A rigid rotation forges a strain of $-\theta^{2}/2$ ¶
  • depends_on example 30.13 A rigid rotation forges a strain of $-\theta^{2}/2$ ¶ ↺
  • depends_on example 30.10 Simple shear and pure shear are the same strain ¶
  • depends_on lemma A.681 Strains under the Kirchhoff hypothesis ¶ ↺
  • depends_on proposition 30.14 Saint-Venant compatibility is necessary ¶
    • depends_on theorem 30.15 Compatibility is sufficient on a simply connected body ¶
  • depends_on proposition 30.8 The trace is the fractional volume change ¶
  • depends_on proposition 30.9 Principal strains ¶
    • depends_on example 30.10 Simple shear and pure shear are the same strain ¶ ↺
  • depends_on proposition 30.7 Strain is a Cartesian tensor of rank two ¶
• depends_on definition 31.8 Rate of strain and vorticity ¶
  • depends_on definition 31.63 Circulation ¶
    • depends_on theorem 31.64 Kelvin's circulation theorem ¶
      • depends_on corollary 31.65 Lagrange: an irrotational flow stays irrotational ¶
        • depends_on remark 31.69 The Kutta condition, and where the circulation comes from ¶
      • depends_on remark 31.66 Only three things make circulation ¶
      • depends_on theorem 31.59 Helmholtz's vortex theorems ¶
        • depends_on corollary 31.65 Lagrange: an irrotational flow stays irrotational ¶ ↺
        • depends_on example 31.60 Vortex rings ¶
  • depends_on definition 31.32 Newtonian fluid; dynamic and kinematic viscosity ¶
    • depends_on remark 31.35 Non-Newtonian fluids are out of scope ¶
    • depends_on remark 31.33 Reading the two viscosities ¶
    • depends_on theorem 31.36 The Newtonian constitutive relation ¶
      • depends_on theorem A.718 Stokes' drag law with its coefficient ¶
      • depends_on theorem 31.37 The Navier–Stokes equations ¶
        • depends_on definition A.741 The statistical setting ¶
        • depends_on definition A.760 The convecting layer ¶
        • depends_on definition 31.43 Creeping flow ¶
        • depends_on phenomenon 31.78 Convective onset at a computed threshold ¶
        • depends_on phenomenon 31.41 The fourth-power law of pipe flow ¶
        • depends_on phenomenon 31.49 Dynamical similarity ¶
        • depends_on proposition A.761 The Boussinesq equations ¶
        • depends_on proposition 31.40 Circular Couette flow ¶
        • depends_on proposition 31.39 Plane Couette flow ¶
        • depends_on remark 31.48 What is actually proved ¶
        • depends_on remark 31.38 Whose equations, and the Stokes hypothesis ¶
        • depends_on theorem A.745 Kármán–Howarth–Monin relation ¶
        • … 3 more
  • depends_on proposition 31.9 Cauchy–Stokes decomposition ¶
    • depends_on remark 31.10 Vorticity is local rotation, not curvature of the path ¶
    • depends_on theorem 31.36 The Newtonian constitutive relation ¶ ↺
• depends_on definition 13.142 Killing tensor ¶
  • depends_on example 13.144 The two Killing tensors every metric carries ¶
  • depends_on theorem 13.143 Killing tensors and geodesic invariants ¶
• depends_on definition 13.111 Linearised curvature of a symmetric field ¶
  • depends_on theorem 13.112 Symmetric analogue of the converse Poincaré lemma ¶