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The Vibrating Ellipse-Shaped Drum

Michael Trott
Organization: Wolfram Research, Inc.
Department: Scientific Information Group
Journal / Anthology

The Mathematica Journal
Year: 1996
Volume: 6
Issue: 4
Page range: 57-63

The Laplace equation for an ellipse is solved by the method of separation of variables. The resulting one-dimensional differential equations are solved with Mathieu functions. The eigenvalues are calculated numerically and the various kinds of eigenmodes are visualized with 3D and contour plots. Some degenerate eigenmodes are explicitly calculated.

*Mathematics > Calculus and Analysis > Differential Equations
*Science > Physics > Mechanics