Semi-Annular Spiral Billiard with Periodic Orbits

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This Demonstration shows spiral-shaped billiard tables patched together using annular pieces. Starting at zero radians on the positive axis, and repeating every
radians counter-clockwise around the spiral, periodic orbits occur where tangents to a table's inner and outer curved boundaries are parallel for the same spiral angle. To construct a table, users can choose the number of loops around the spiral and the rate at which the width of the spiral increases.
Contributed by: William C. Hill (March 2012)
Open content licensed under CC BY-NC-SA
Snapshots
Details
The trajectory calculations are based on figure 1 on page 539 of [1].
Reference
[1] J. S. Espinoza Ortiz and R. Egydio de Carvalho, "Energy Spectrum and Eigenfunctions through the Quantum Section Method," Brazilian Journal of Physics, 31(4), 2001 pp. 538–545.
Permanent Citation