## An Animated Discussion about Pendulums

I was in Boston last week attending the ASME International Mechanical Engineering conference demonstrating MapleSim, our new tool for physical modeling.  I had the opportunity to speak to a large number of delegates, but I remember one conversation in particular; a professor who taught freshman students was bemoaning the fact that he found it harder and harder to impress students with his relatively simple animations of physics phenomena.  A simple animated pendulum no longer captivated students who were already immersed in the interactive physics-enabled environments of video games.  He had to escalate the intricacy of his demonstrations, but generating them was starting to consume too much of his time.

So, faced with a four hour wait at Boston Logan airport on the return leg of my journey, I decided to see how far I could push the concept of an animated pendulum.  It was clear that two and three link pendulums were as boring as single pendulums, so upped the ante to a nine-link pendulum (I simply plucked that number out of the ether).

Deriving the equations by hand for a two-link pendulum is hard enough for someone of my meagre abilities, so I decided to see if I could put MapleSim to use.   (After all, one of its major benefits is that it automatically generates the system equations for multibody systems.)

So with MapleSim I created a model of a nine-link pendulum (adding damping at each of the joints for no other reason than I could).  Here’s a screengrab of the MapleSim model.

Switching to Maple (via a menu option in MapleSim), and issuing a few commands gave me the optimized symbolic representation of the dynamic equations.  A call to dsolve and a few plot commands later resulted in this animation.

I was pleasantly surprised to discover that the tumbling of its body and the small flicks of the tail resembles a tethered rope.  It’s not quite the interactive object that students commonly see in video games, but hey, it certainly beats a bob on a line swinging back and forth!

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