Sunday, May 1, 2011

Week TechVideo, 2011 #17 - Double Pendulum

We all knew already how helpful LEGO Technic might be to demonstrate some mathematical properties.
Yet, with this infinitely simple construction we get also a demonstration from the chaotic behavior of the Double Pendulum.



In mathematics a double pendulum is a pendulum with another pendulum attached to its end, and is a simple physical system that exhibits rich dynamic behavior with strong sensitivity to the initial conditions.

The motion of a double pendulum is governed by a set of coupled ordinary differential equations. For small angles, the double pendulum behaves like a linear system. However for large angles or certain energies, the double pendulum is non-linear and its motion turns chaotic.

8 comments:

Anonymous said...

what is your education background may i ask??

Conchas said...

Engineering Physics (EP). Why?

Junkstyle Gio said...

There used to be a small toy that worked on that principle..

Mark Bellis said...

In the Electronics department of my old university (York, UK) there is a chaotic pendulum with a 'T' shape. The first pendulum has three arms of the 'T', with similar single-arm second pendulums on the ends of each arm. If you wind it up fast enough it goes on for 20 minutes or so. Not so easy to create a pendulum with low enough friction from LEGO parts though.
It is possible to make a LEGO chaotic system that includes electrical power inputs and motors, maybe with NXT feedback too, to overcome friction in the system. The use of a "-x^2" term in an equation in the NXT would invite chaos - that term is in the population curve and Mandelbrot chaotic equations. This is known in real control systems and such chaos often has to be damped out.
A Power Functions system could do it with motors controlling the handsets for each other's IR receivers, like this: http://www.brickshelf.com/cgi-bin/gallery.cgi?f=241795
It might be possible in pneumatics too. My pneumatic servo http://www.brickshelf.com/cgi-bin/gallery.cgi?f=405269 could be made chaotic, given more gain. Since it uses a non-regulated pressure and a compressible medium, the valve movement is in proportion to the acceleration of the cylinder movement, representing a double integration in the control loop. With a regulated pressure of a non-compressible fluid (hydraulics) it would be proportional to the velocity of the cylinder, a single integration. Both are capable of chaotic behaviour.

Anonymous said...

>>Engineering Physics (EP). Why?
I was just wondering, cause your blog has an interesting mix of engineering and maths, thanks!

thomas said...

I am not sure if I understand the point of this?

Menno Gorter said...

http://www.youtube.com/watch?v=C-rJm3E6wtM

;-)

Conchas said...

Incredible! :)

Related Posts Plugin for WordPress, Blogger...



© 2007-2014 TechnicBRICKs
TechnicBRICKs contents may be sporadically updated, if the authors finds further relevant info about a certain post, or content/spell mistakes. Hence please don't be surprised if you find few changes at later visits, relative to a previous read.

TechnicBRICKs often shows other peoples' creations and/or images. We always try to credit the author(s) and link to their main publishing website, and if possible with their name in real life.
Since this is not always possible, we request that if you find something here that is yours or from someone you know, you leave a comment on the respective post and claim the authorship.

TechnicBRICKs is optimized for Firefox 16.0 and 1600x1200 resolution displays or wider.

LEGO® is a trademark of The LEGO Group of companies which does not sponsor, authorize or endorse this blog.
LEGO, the LEGO logo, the Brick and Knob configurations, the Minifigure and MINDSTORMS, are registered trademarks of The LEGO Group.
Original LEGO images are copyrighted by The LEGO Group and are used here in accordance with their fair play policy.
You can visit the official LEGO® website at www.LEGO.com.