definition 13.3 Orthogonal coordinate system

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• depends_on definition 13.4 Orthogonal coordinate transformation ¶
  • depends_on definition 13.5 Tensor under orthogonal transformations ¶
    • depends_on definition 19.42 Inertia tensor ¶
      • depends_on definition 29.13 Inertia tensor, continuum form ¶
        • depends_on definition 29.19 Inertia ellipsoid ¶
        • depends_on example 29.23 The polar moment of the Earth, and what it reveals ¶
        • depends_on proposition 49.17 Magnetic-dipole spin-down ¶
        • depends_on proposition 29.14 Angular momentum and kinetic energy ¶
        • depends_on proposition 29.15 Positivity ¶
        • depends_on proposition 29.24 MacCullagh's formula ¶
        • depends_on proposition 29.22 Perpendicular-axis theorem ¶
        • depends_on theorem 29.20 Parallel-axis theorem ¶
        • depends_on theorem 29.16 Principal axes ¶
      • depends_on example 19.45 The uniform solid sphere ¶
      • depends_on proposition 19.43 The moment of inertia is a quadratic form in the axis ¶
    • depends_on definition 29.13 Inertia tensor, continuum form ¶ ↺
    • depends_on lemma 30.26 Isotropic Cartesian tensors of rank four ¶
      • depends_on phenomenon 30.28 Hooke's law ¶
        • depends_on phenomenon 30.32 Poisson contraction ¶
        • depends_on remark 30.78 Anharmonicity: what the quadratic energy also suppresses ¶
    • depends_on notation 30.1 Strain and displacement share a letter ¶
    • depends_on proposition 30.7 Strain is a Cartesian tensor of rank two ¶
    • depends_on proposition 13.96 The cross product is an axial vector ¶
    • depends_on proposition 13.6 Levi-Civita identities in three dimensions ¶
      • depends_on proposition 13.96 The cross product is an axial vector ¶ ↺
      • depends_on proposition 13.95 The elementary cross-product identities ¶
    • depends_on proposition 19.43 The moment of inertia is a quadratic form in the axis ¶ ↺
    • depends_on remark 13.7 What the classification is used for ¶
    • depends_on theorem 30.18 Cauchy: the stress tensor exists ¶
      • depends_on definition 30.24 The elasticity tensor ¶
        • depends_on definition 30.37 Voigt notation ¶
        • depends_on phenomenon 30.28 Hooke's law ¶ ↺
        • depends_on proposition 30.25 Twenty-one constants ¶
        • 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 31.1 Fluid ¶
        • depends_on definition 31.21 Ideal fluid ¶
        • depends_on definition 31.2 Knudsen number ¶
        • depends_on definition 31.32 Newtonian fluid; dynamic and kinematic viscosity ¶
        • depends_on proposition 31.16 Hydrostatic balance ¶
      • depends_on proposition 30.19 The stress tensor is symmetric ¶
        • depends_on definition 30.20 Pressure and deviatoric stress ¶
      • depends_on proposition 30.74 The maximum shear stress, and its indifference to pressure ¶
        • depends_on phenomenon 30.73 Yield and brittle fracture ¶
        • depends_on remark A.705 The dangerous stress is below the surface ¶
        • depends_on remark 30.75 Two criteria, one uncited ¶
      • depends_on remark 30.72 Stress concentration ¶
        • depends_on proposition 30.76 Griffith's criterion ¶
      • depends_on theorem A.695 Boussinesq's point-force solution, quoted ¶
        • depends_on definition A.698 The Hertz contact problem ¶
        • depends_on lemma A.697 Surface displacement under a distributed pressure ¶
      • depends_on theorem 30.21 Cauchy's equation of motion ¶
        • depends_on definition 30.22 Boundary conditions of elastostatics ¶
        • depends_on proposition 30.23 Virtual work; the weak form ¶
        • depends_on proposition 31.16 Hydrostatic balance ¶ ↺
        • depends_on remark 30.69 Saint-Venant's principle, and its exact status ¶
        • depends_on theorem 30.40 Navier–Cauchy equations ¶
        • depends_on theorem 31.22 Euler's equations of motion ¶