equation 16.18 eq:calcvar-dbr-hyp

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Supports

• depends_on lemma 16.19 du Bois-Reymond ¶
  • depends_on lemma 16.20 Mixed form ¶
    • 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 proposition 21.56 The two prescriptions and their difference ¶
    • 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 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 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 ¶ ↺