equation 7.177 eq:ana-functional-derivative

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Supports

• depends_on definition 16.15 Variation; the first variation ¶
  • depends_on definition 16.83 One-parameter transformation group; variational symmetry ¶
  • depends_on lemma 16.18 Fundamental lemma ¶
    • 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 remark A.692 The corner force is real, and you can feel it ¶
    • depends_on theorem 16.36 Euler–Lagrange equations for several independent variables ¶
      • depends_on definition 44.6 Stress–energy tensor ¶
        • depends_on definition 44.36 Energy conditions ¶
        • depends_on proposition 44.17 Stress–energy of the electromagnetic field ¶
        • depends_on theorem 44.19 Covariant conservation of stress–energy ¶
        • depends_on theorem 44.9 Variation of the Einstein–Hilbert action ¶
      • depends_on proposition 28.42 The wave equation of a stretched string ¶
    • depends_on theorem 16.38 Euler–Poisson equation ¶
      • depends_on theorem 30.56 The beam equation ¶
        • depends_on example 30.58 A steel ruler ¶
        • depends_on proposition 30.57 Bending waves are dispersive ¶
      • depends_on theorem 30.64 The Kirchhoff plate equation ¶
        • depends_on phenomenon 30.65 Chladni figures ¶
        • depends_on proposition 30.66 Chladni scaling ¶
        • depends_on remark 30.67 Germain, Kirchhoff, and the edge conditions ¶
    • depends_on theorem 16.41 Multiplier rule for pointwise constraints ¶
      • depends_on proposition 21.56 The two prescriptions and their difference ¶
    • depends_on theorem 16.31 Natural boundary condition ¶
      • depends_on remark 30.67 Germain, Kirchhoff, and the edge conditions ¶ ↺
      • depends_on theorem A.691 Kirchhoff's edge conditions and the corner force ¶ ↺
      • depends_on theorem 16.32 Transversality ¶
        • depends_on corollary 16.33 Weierstrass–Erdmann corner conditions ¶
    • depends_on theorem 25.19 Hamilton's equations from the first-order action ¶
    • depends_on theorem 25.22 Faddeev–Jackiw equations and brackets ¶
      • depends_on example 25.24 A charged particle in a strong magnetic field ¶
  • depends_on proposition 16.16 Stationarity is necessary ¶
    • depends_on theorem 16.22 Euler–Lagrange ¶
      • depends_on definition 16.62 Field of extremals; slope function ¶
        • depends_on definition 23.52 Lagrangian family; caustic ¶
        • depends_on remark 23.8 The action as a function, not a functional ¶
        • depends_on theorem 16.63 Hilbert's invariant integral ¶
        • depends_on theorem 16.64 Weierstrass' sufficient condition ¶
      • depends_on phenomenon 30.52 Euler buckling ¶
        • depends_on example 30.53 A steel rod buckles at a twentieth of its crushing load ¶
        • depends_on remark 30.54 Other end conditions, and what buckling is variationally ¶
        • depends_on remark 30.55 Beyond the critical load: the elastica ¶
        • depends_on remark 30.68 Shells carry load in a different way ¶
      • depends_on proposition 29.39 Steady precession ¶
      • depends_on theorem 16.35 System of Euler–Lagrange equations ¶
        • depends_on proposition 16.6 The isoperimetric extremal is a circle ¶
        • depends_on theorem 16.41 Multiplier rule for pointwise constraints ¶ ↺
      • depends_on theorem 16.31 Natural boundary condition ¶ ↺
    • depends_on theorem 16.51 Legendre's necessary condition ¶
      • depends_on corollary 16.65 Sufficiency for a weak minimum ¶
      • depends_on theorem 16.55 Jacobi's necessary condition ¶
        • depends_on proposition 23.53 A caustic point is a conjugate point ¶
        • depends_on remark 30.54 Other end conditions, and what buckling is variationally ¶ ↺
  • depends_on theorem 16.43 Euler's rule for integral constraints ¶
    • depends_on example 16.45 Two solved isoperimetric problems ¶
    • depends_on proposition 16.4 The hanging chain is a catenary ¶
    • depends_on proposition 16.6 The isoperimetric extremal is a circle ¶ ↺