remark 30.59 Where Euler–Bernoulli fails

Rests on

• depends_on equation 30.35 eq:elast-wave-speeds ¶
• depends_on proposition 30.57 Bending waves are dispersive ¶
  • depends_on definition 9.2 Linear equation; homogeneity ¶
    • depends_on definition 9.1 Ordinary differential equation ¶
  • depends_on theorem 30.56 The beam equation ¶
    • depends_on proposition 30.51 Moment and curvature ¶
      • depends_on definition 30.31 The engineering moduli ¶
        • depends_on definition 30.20 Pressure and deviatoric stress ¶
        • depends_on equation 30.21 eq:elast-hooke-isotropic ¶
      • depends_on equation 30.21 eq:elast-hooke-isotropic ¶ ↺
      • proves proof ch:13-continuum-elasticity@proof-27 ¶
    • depends_on theorem 16.38 Euler–Poisson equation ¶
      • depends_on corollary 7.44 Substitution and integration by parts ¶
        • depends_on proposition 7.31 Chain rule ¶
        • depends_on proposition 7.30 Leibniz rule ¶
        • depends_on theorem 7.43 Fundamental theorem of calculus, II ¶
        • proves proof ch:05-real-analysis@proof-26 ¶
      • depends_on equation 16.15 eq:calcvar-first-variation ¶
      • depends_on lemma 16.18 Fundamental lemma ¶
        • depends_on definition 16.15 Variation; the first variation ¶
        • depends_on theorem 7.40 Continuous functions are integrable ¶
        • proves proof ch:14-calculus-of-variations@proof-8 ¶
      • proves proof ch:14-calculus-of-variations@proof-21 ¶
    • proves proof ch:13-continuum-elasticity@proof-29 ¶
  • proves proof ch:13-continuum-elasticity@proof-30 ¶

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