Pleat Swing Physics?

[Bugbear]

If you are saying that a strip of fabric, with no weight added to the bottom is a pendulum, then fine.
If you can consider a string hanging from a tack in the ceiling, with no weight at the bottom, to be a pendulum, then fine.
There is a uniform weight per square measurement from the bottom of the fell to the bottom of the pleat; that's not counting a hemmed pleat.

[Dixiecat]

Now, to similate the fore-and-aft motion of the legs, rigidly fix out-of-phase sinusoidal fore-and-aft drivers to the end pendula. These have the same/opposite phase as the top driver

Did you add in the Coriolis Effect? Air Resistance?

[ronstew]

If you are saying that a strip of fabric, with no weight added to the bottom is a pendulum, then fine.

The pendulum with a string of negligible mass and a high-density bob is called an ideal pendulum. A physical pendulum has mass along its lenth, so moments of inertia must be considered. I am proposing a uniform physical pendulum, which has the same linear density along its length. I am imagining the strip of cloth modeled as rigid, with a pivot at the top.

Consider the old physicist joke:

There is this farmer who is having problems with his chickens. All of the sudden, they are all getting very sick and he doesn't know what is wrong with them. After trying all conventional means, he calls a biologist, a chemist, and a physicist to see if they can figure out what is wrong. So the biologist looks at the chickens, examines them a bit, and says he has no clue what could be wrong with them. Then the chemist takes some tests and makes some measurements, but he can't come to any conclusions either. So the physicist tries. He stands there and looks at the chickens for a long time without touching them or anything. Then all of the sudden he starts scribbling away in a notebook. Finally, after several gruesome calculations, he exclaims, 'I've got it! But it only works for spherical chickens in a vacuum.'

Idea being, if you want to create a physics model of a real, complex system, start with a simplified approximation. Solve it, then add a complication. Solve and repeat.

Anyay, this probably has been done already. Watch Shrek or any computer-animated film with a woman in a flowing skirt. Animation companies pay physicists and mathematicians to create effects like this. Somebody at Industrial Light and Magic, Pixar or Dreamworks probably has a pleated skirt model at the ready.

[george7]

Something to play with.
http://www.custom-logic.com/exp/cloth/cloth.html
http://www.lhup.edu/~dsimanek/scenario/newton.htm

[ronstew]

Something to play with.
http://www.custom-logic.com/exp/cloth/cloth.html
http://www.lhup.edu/~dsimanek/scenario/newton.htm

Wow. That first one verifies my last point.

[Bugbear]

Oh no... not the Coriolis Effect myth again.

Anyway, I still think the movement of the pleats has a lot to do with the slight springy-ness of the fabric.

[tyger]

Anyway, I still think the movement of the pleats has a lot to do with the slight springy-ness of the fabric.

You must be correct. If the fabric were infinitely not springy (therefore, totally rigid), wouldn't swing be affected? Likewise, if the fabric were infinitely springy (therefore, totally 'plastic', not elastic), wouldn't swing be affected?

[Bugbear]

Yes, I know... the Earth is flat.

[Bugbear]

By the way, the egg was around way, way before the chicken came on the scene.

[ChattanCat]

There are three parts to a pleat. Let's say that we have a kilt that is pleated to the stripe to make my explaination easier. So, lets look at one pleat. A pleat is shaped in a Z. The top of the Z is the stripe. The bottom of the Z is actually the next pleat. It is my hypothesis that the middle section of the Z is the leaf spring. It will bend when pulled on by the upper and lower legs of the Z. With 29 pleats, each pleat will only have to open 0.2" to have a total 6" swing of the outside pleat.