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1: 19.35 Other Applications

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§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

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3: 21.9 Integrable Equations

§21.9 Integrable Equations

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4: 9.16 Physical Applications

… ►In fluid dynamics, Airy functions enter several topics. …

5: Bibliography P

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A First Course in Fluid Dynamics. Cambridge University Press, Cambridge.

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External Links:

ISBN 0-521-25416-7; 0-521-27424-9, MathReview, ZentralBlatt

Referenced by:

§18.39(v).

Encodings:

BibTeX

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6: 18.39 Applications in the Physical Sciences

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§18.39(v) 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). …

7: Bibliography W

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A Treatise on the Analytical Dynamics of Particles and Rigid Bodies. 4th edition, Cambridge University Press, Cambridge.

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Notes:

Reprinted in 1988.

External Links:

ISBN 0-521-35883-3, MathReview, ZentralBlatt

Referenced by:

§22.19(i), §22.19(iv), §22.19(v), §23.21(i).

Encodings:

BibTeX

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A presentation of cnoidal wave theory for practical application. J. Fluid Mech. 7 (2), pp. 273–286.

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External Links:

Document, MathReview (T. B. Benjamin), ZentralBlatt

Referenced by:

§21.9.

Encodings:

BibTeX

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8: 28.33 Physical Applications

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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.

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

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9: 22.19 Physical Applications

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§22.19(i) Classical Dynamics: The Pendulum

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§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). …