I recently aquired these fabulous ballet flats (on sale!) for everyday street wear and it made me wonder about the physics of ballet shoes and ballet in general. I found this great website that applies and explains ballet moves in mathematical terms, www.unc.edu/~shahk/Sites/Site/Welcome.html
I encourage you to check it out as it was quite enjoyable to read. Each tab on the page explains a different element of ballet from the shoes to the graceful (and illusory!) leaps.
For even more details and some great references check out this website http://www.hep.uiuc.edu/home/g-gollin/dance/dance_physics.html
If you want to read about Yale professors who put the calculations in choreography check out http://www.symmetrymagazine.org/article/may-2014/the-physics-of-dance
And if you want to read even more, check out this student paper
http://arxiv.org/pdf/0706.2717.pdf or this book (available on Amazon)
As for me I think it is time to practice rotational inertia.
Happy STEM dancing!