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1: 19.35 Other Applications
§19.35(ii) Physical
Elliptic integrals appear in lattice models of critical phenomena (Guttmann and Prellberg (1993)); theories of layered materials (Parkinson (1969)); fluid dynamics (Kida (1981)); string theory (Arutyunov and Staudacher (2004)); astrophysics (Dexter and Agol (2009)). …
2: 11.12 Physical Applications
§11.12 Physical Applications
3: 18.39 Physical Applications
§18.39(ii) Other Applications
For applications of Legendre polynomials in fluid dynamics to study the flow around the outside of a puff of hot gas rising through the air, see Paterson (1983). …
4: 21.9 Integrable Equations
§21.9 Integrable Equations
5: 9.16 Physical Applications
In fluid dynamics, Airy functions enter several topics. …
6: Bibliography P
  • A. R. Paterson (1983) A First Course in Fluid Dynamics. Cambridge University Press, Cambridge.
  • 7: Bibliography W
  • E. T. Whittaker (1964) A Treatise on the Analytical Dynamics of Particles and Rigid Bodies. 4th edition, Cambridge University Press, Cambridge.
  • R. L. Wiegel (1960) A presentation of cnoidal wave theory for practical application. J. Fluid Mech. 7 (2), pp. 273–286.
  • 8: 28.33 Physical Applications
  • McLachlan (1947, Chapters XVI–XIX) for applications of the wave equation to vibrational systems, electrical and thermal diffusion, electromagnetic wave guides, elliptical cylinders in viscous fluids, and diffraction of sound and electromagnetic waves.

  • McLachlan (1947, Chapter XV) for amplitude distortion in moving-coil loud-speakers, frequency modulation, dynamical systems, and vibration of stretched strings.

  • 9: 22.19 Physical Applications
    §22.19(i) Classical Dynamics: The Pendulum
    §22.19(ii) Classical Dynamics: The Quartic Oscillator
    Its dynamics for purely imaginary time is connected to the theory of instantons (Itzykson and Zuber (1980, p. 572), Schäfer and Shuryak (1998)), to WKB theory, and to large-order perturbation theory (Bender and Wu (1973), Simon (1982)). …
    §22.19(v) Other Applications
    Numerous other physical or engineering applications involving Jacobian elliptic functions, and their inverses, to problems of classical dynamics, electrostatics, and hydrodynamics appear in Bowman (1953, Chapters VII and VIII) and Lawden (1989, Chapter 5). …