5 ms·

A pendulum theorem

58 points by mgdo 10y ago

selimthegrim 10y ago
This isn't original to Acheson - the single pendulum case is widely known as the Kapitza pendulum. https://en.wikipedia.org/wiki/Kapitza%27s_pendulum https://en.wikipedia.org/wiki/Kapitza%27s_pendulum If you speak Russian the following video with V.I. Arnold is nice http://www.youtube.com/watch?v=ZBSLK3Jbd2I http://www.youtube.com/watch?v=ZBSLK3Jbd2I
- ars 10y ago
  This one is in English: https://www.youtube.com/watch?v=gnn21smGVrQ https://www.youtube.com/watch?v=gnn21smGVrQ
- jacobolus 10y ago
  The paper says in its first sentence “Stephenson (1908a, b) showed that it is possible ... He confirmed his theoretical predictions by a practical demonstration ...”
  - selimthegrim 10y ago
    His derivation isn't nearly as complete as Kapitza's, though.
idlewords 10y ago
The last line of the paper mentions seeing a triple inverted pendulum recover from even very severe perturbations and go back to vertical. I would love to see a video of this stuff!
- dools 10y ago
  This is a different control mechanism but it's still a cool video :) https://www.youtube.com/watch?v=cyN-CRNrb3E https://www.youtube.com/watch?v=cyN-CRNrb3E
  - curiousgal 10y ago
    Came across this video after watching that, somehow related but equally amazing. https://www.youtube.com/watch?v=Lt-KLtkDlh8 https://www.youtube.com/watch?v=Lt-KLtkDlh8
- aji 10y ago
  this one was linked by ars elsewhere in the comments here. references the paper as well. very cool! https://www.youtube.com/watch?v=gnn21smGVrQ https://www.youtube.com/watch?v=gnn21smGVrQ
Jun8 10y ago
Hmm, this reminded me of an empirical discovery I made: When walking with an open coffee cup at hand oscillating your hand vertically in random fashion greatly reduces the coffee resonance and the sloshing effect. This problem has been investigated before (http://www.sciencemag.org/news/2012/05/physics-spilled-coffee http://www.sciencemag.org/news/2012/05/physics-spilled-coffe...) but AFAIK the above solution has not been proposed. I wonder if the theorem given can help motivate this finding?
- adrianN 10y ago
  Walk without rythm and we won't spill the coffee.
- gaze 10y ago
  This is a funny example of spread spectrum modulation. You're decreasing the energy at the frequency of the sloshing mode by modulating it with random noise.
elcritch 10y ago
Makes me think about drones in particular. If you can control an inverted n-ary pendulum then controlling inverted thrust should be a straightforward extension.
Animats 10y ago
When that was discovered it was a shock to the controls community. Inverted pendulum stabilization was long thought to require active control. Here's a video demonstrating passive stabilization.[1] It's so simple it's embarrassing. [1] https://www.youtube.com/watch?v=rwGAzy0noU0 https://www.youtube.com/watch?v=rwGAzy0noU0
akssri 10y ago
Mark Levi has written about these things on SIAM and has a nice video up on, http://www.personal.psu.edu/mxl48/Inverted_Pendulum.html http://www.personal.psu.edu/mxl48/Inverted_Pendulum.html I think they've also shown that this is robustly stable for a particular family.
1jFDS 10y ago
Sane link: http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.205.5342&rep=rep1&type=pdf http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.205... I don't understand how people put up with a wobbling "Click here to see more" on fermatslibrary.com. What is next? Back to marquee?

58 points by mgdo 10y ago

This isn't original to Acheson - the single pendulum case is widely known as the Kapitza pendulum. https://en.wikipedia.org/wiki/Kapitza%27s_pendulum https://en.wikipedia.org/wiki/Kapitza%27s_pendulum If you speak Russian the following video with V.I. Arnold is nice http://www.youtube.com/watch?v=ZBSLK3Jbd2I http://www.youtube.com/watch?v=ZBSLK3Jbd2I

ars 10y ago
This one is in English: https://www.youtube.com/watch?v=gnn21smGVrQ https://www.youtube.com/watch?v=gnn21smGVrQ
jacobolus 10y ago
The paper says in its first sentence “Stephenson (1908a, b) showed that it is possible ... He confirmed his theoretical predictions by a practical demonstration ...”
- selimthegrim 10y ago
  His derivation isn't nearly as complete as Kapitza's, though.

idlewords 10y ago

The last line of the paper mentions seeing a triple inverted pendulum recover from even very severe perturbations and go back to vertical. I would love to see a video of this stuff!

dools 10y ago
This is a different control mechanism but it's still a cool video :) https://www.youtube.com/watch?v=cyN-CRNrb3E https://www.youtube.com/watch?v=cyN-CRNrb3E
- curiousgal 10y ago
  Came across this video after watching that, somehow related but equally amazing. https://www.youtube.com/watch?v=Lt-KLtkDlh8 https://www.youtube.com/watch?v=Lt-KLtkDlh8
aji 10y ago
this one was linked by ars elsewhere in the comments here. references the paper as well. very cool! https://www.youtube.com/watch?v=gnn21smGVrQ https://www.youtube.com/watch?v=gnn21smGVrQ

Jun8 10y ago

Hmm, this reminded me of an empirical discovery I made: When walking with an open coffee cup at hand oscillating your hand vertically in random fashion greatly reduces the coffee resonance and the sloshing effect. This problem has been investigated before (http://www.sciencemag.org/news/2012/05/physics-spilled-coffee http://www.sciencemag.org/news/2012/05/physics-spilled-coffe...) but AFAIK the above solution has not been proposed. I wonder if the theorem given can help motivate this finding?

adrianN 10y ago
Walk without rythm and we won't spill the coffee.
gaze 10y ago
This is a funny example of spread spectrum modulation. You're decreasing the energy at the frequency of the sloshing mode by modulating it with random noise.

elcritch 10y ago

Makes me think about drones in particular. If you can control an inverted n-ary pendulum then controlling inverted thrust should be a straightforward extension.

Animats 10y ago

When that was discovered it was a shock to the controls community. Inverted pendulum stabilization was long thought to require active control. Here's a video demonstrating passive stabilization.[1] It's so simple it's embarrassing. [1] https://www.youtube.com/watch?v=rwGAzy0noU0 https://www.youtube.com/watch?v=rwGAzy0noU0

akssri 10y ago

Mark Levi has written about these things on SIAM and has a nice video up on, http://www.personal.psu.edu/mxl48/Inverted_Pendulum.html http://www.personal.psu.edu/mxl48/Inverted_Pendulum.html I think they've also shown that this is robustly stable for a particular family.

1jFDS 10y ago

Sane link: http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.205.5342&rep=rep1&type=pdf http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.205... I don't understand how people put up with a wobbling "Click here to see more" on fermatslibrary.com. What is next? Back to marquee?