{"id":3264,"date":"2014-02-05T18:24:35","date_gmt":"2014-02-05T23:24:35","guid":{"rendered":"https:\/\/blogs.mathworks.com\/seth\/?p=3264"},"modified":"2014-02-10T09:02:25","modified_gmt":"2014-02-10T14:02:25","slug":"win-olympic-gold-with-simmechanics-modeling-figure-skating-and-angular-momentum","status":"publish","type":"post","link":"https:\/\/blogs.mathworks.com\/simulink\/2014\/02\/05\/win-olympic-gold-with-simmechanics-modeling-figure-skating-and-angular-momentum\/","title":{"rendered":"Win Olympic Gold with SimMechanics: Modeling Figure Skating and Angular Momentum"},"content":{"rendered":"

With the XXII Winter Olympics starting this week, I thought we should take the time to model something from the games! So lets look at how conservation of angular momentum is important in figure skating.<\/p>\r\n\r\n

The problem<\/strong><\/p>\r\n\r\n

Some time ago a user asked me to illustrate the conservation of angular momentum<\/a> in SimMechanics<\/a>. In my opinion, there is no better application to illustrate this phenomenon then a figure skater spinning. As you are probably aware, when a figure skater spins, bringing her arms closer or further from her body changes the speed at which she spins.<\/p>\r\n\r\n

\"Conservation
\r\nOpenStax College - Angular Momentum and Its Conservation - http:\/\/cnx.org\/content\/m42182\/1.5\/<\/a><\/em><\/p>\r\n\r\n

It's pretty simple, the angular momentum, which is the product of the angular velocity and the moment of inertia remains constant. If one increases, the other must decrease.<\/p>\r\n\r\n

A Simple SimMechanics Version<\/strong><\/p>\r\n\r\n

Before implementing a complete figure skater, I thought it would be a good idea to begin by the simplest model highlighting conversation of angular momentum. Here is what it looks like:<\/p>\r\n\r\n

\"Conservation<\/p>\r\n\r\n

As you can see, I use a a prismatic joint<\/a> to change the distance of a body from the center of rotation around a Revolute joint<\/a>. When looking at the results, we can see that the rotation speed increases when the body comes closer to the center.<\/p>\r\n\r\n

\"Conservation<\/p>\r\n\r\n

The Spinning Skater<\/strong><\/p>\r\n\r\n

To make my simulation closer to what you will see during the Olympics, I modeled a simple skater using 2 cylinders for the legs, 1 large cylinder for the body, and two cylinders for the arms. I attached the legs and arms to the body using revolute joints. To apply the spinning motion, I attach one leg to the ground using a revolute joint, and I simply give this revolute an initial angular velocity.<\/p>\r\n\r\n

\"Conservation<\/p>\r\n\r\n

During the simulation, I first make the leg go down, accelerating the body a little. A few seconds after, I make both arms go closer to the body, reducing the moment of inertia and accelerating the body more significantly. Here is what it looks like:<\/p>\r\n\r\n

\"Conservation<\/p>\r\n\r\n

Update:<\/strong> Download the models used in this post here:\r\n