Wired Broadband and Related Industry Glossary of Terms with Acronyms As of 13 June 2011 Compiled By: Conrad L. Young, Director, Broadband Technical Strategy



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They are sometimes known as Bowditch curves after Nathaniel Bowditch, who studied them in 1815. They were studied in more detail (independently) by Jules-Antoine Lissajous in 1857 (MacTutor Archive). Lissajous curves have applications in physics, astronomy, engineering, and other sciences. The curves close if is rational.

Lissajous curves are a special case of the harmonograph with damping constants .

Examples of Lissajous Curves, courtesy of Weisstein, Eric W. "Lissajous Curve." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/LissajousCurve.html


Special cases are summarized in the following table, and include the line, circle, ellipse, and section of a parabola.

parameters

curve

,

line

, ,

circle

, ,

ellipse

,

section of a parabola


The line, circle, ellipse, and section of a parabola; all special cases of the Lissajou Curve courtesy of Weisstein, Eric W. "Lissajous Curve." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/LissajousCurve.html


REFERENCES:

  1. Cundy, H. and Rollett, A. "Lissajous's Figures." §5.5.3 in Mathematical Models, 3rd ed. Stradbroke, England: Tarquin Pub., pp. 242-244, 1989.

  2. Gray, A. Modern Differential Geometry of Curves and Surfaces with Mathematica, 2nd ed. Boca Raton, FL: CRC Press, pp. 70-71, 1997.

  3. Lawrence, J. D. A Catalog of Special Plane Curves. New York: Dover, pp. 178-179 and 181-183, 1972.

  4. MacTutor History of Mathematics Archive. "Lissajou Curves." http://www-groups.dcs.st-and.ac.uk/~history/Curves/Lissajous.html.

  5. Wells, D. The Penguin Dictionary of Curious and Interesting Geometry. London: Penguin, p. 142, 1991.

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