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I am performing a mathematical exploration into the mathematics of ballet. I began by examining the fouetté turns and I thought that the shape/structure created when the ballet turns would be a helix. However, my further research led me to the following video

https://www.youtube.com/watch?v=l5VgOdgptRg

Using this I began looking at the ballerina as a spinning top while she performs the fouetté turn. I would like to graph this 3D shape ,created by the ballerina when she turns, on a graphing software such as Autograph. However, I am unable to figure out the equation of a spinning top or how to graph it. Is there a specific mathematical name or equation for the shape of a spinning top? How can it be graphed?

Pallavi
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  • Are you talking a spinning top like in Inception? – AlgorithmsX Nov 04 '16 at 13:08
  • What do yo mean by shape? Every point of a spinning top follows a circular trajectory (at most an epicycle), at least when the rotation is stable. In the case of the ballerina are you interested in graphing the trajectory of her up foot? – Ana S. H. Nov 04 '16 at 13:13
  • So by shape, I'm looking to graph a shape similar to

    https://thumb1.shutterstock.com/display_pic_with_logo/169/490307758/stock-vector-spinning-top-toy-490307758.jpg

    This is assuming a stable axis of rotation. For instance, if the dancer in the following picture is rotated about a stable axis (namely the leg on the ground) what structure would be described by the other bent leg which is rotating?

    http://pad1.whstatic.com/images/thumb/f/f9/Do-Ballet-Fouette-Turns-Step-2.jpg/aid2053216-728px-Do-Ballet-Fouette-Turns-Step-2.jpg

     – Pallavi Nov 04 '16 at 13:19

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Your question is best explained by the following link: http://www.mathematica-journal.com/2012/02/motion-of-a-spinning-top/. Also the following link would help: http://www.maths.surrey.ac.uk/explore/michaelspages/Spin.htm.