In December, I wrote about finding a Mathemetica notebook that helped me start to understand the classic Inverted Pendulum problem as it relates to the Woodside-One-Wheelers learning to turn themselves into stable inverted pendulums.
With the release of Mathematic 8, Andrew Moylan, a Mathematica employee, has created blog presentations highlighting its new features. He has written Stabilized Inverted Pendulum and Stabilized n-link Pendulum. In the first article, he describes Mathematica's capacity in terms that make sense to me and perhaps to some of our ITeam members:
Using the new control systems features (one of several new application areas integrated into Mathematica 8), I’ve been experimenting with models of stabilized inverted pendulums. I’m no expert in control theory, but you’ll see that one doesn’t need to be.
I'm no expert in unicycling, physics, control theory, or any other arcane elements of this story but I don't need to be to appreciate and explore the connections. And, I suspect that our ITeam students don't need to be experts either to find some age-appropriate insight into something that catches their interest.
The Bowdoin Robotics Team came to Mt. Ararat Middle School last week and inspired several middle school students to think more about balancing on one foot (inverted pendulum with fixed base) to kick a soccer ball. Matt worked in ITeam meetings, CET, at home in the evening to install and start to learn Python because the Bowdoin Team uses it to control their robots!
Moylan include several video clips (generated with Mathematica) in order to illustrate the ideas he discusses. He also includes a link to the notebook that he created. Inside the notebook, he hints at even greater support for explorations by experts-in-training.
In the next article in this series, we'll derive pendulum-and-cart equations programmatically to make it easy to explore more general cases.
Samuel Chen commented on Moylan's post with this observation:
Simply amazing! One single post from Moylan covers the entire mechanics course from college!
Compare that with Sophia.org's concept of learning packets.
The material on Sophia is organized by "learning packets," which are small, bite-sized tutorials focused around a specific learning objective, including thousands of standards-aligned objectives. Each packet includes a question and answer conversation, giving learners the benefit of learning from both the content itself as well as the supplementary discussion.I'm finishing this post now so that I can go and explore Moylan's notebooks with the new Mathematica CDF player.