Pleat Swing Physics?

[ronstew]

It's not doctoral stuff, but a reasonable model would be a high-end undergraduate problem. Consider thirty uniform physical pendula arranged in a line, each rigidly fixed at the top, linked with a horizontal low-constant spring to the next one midway up. The tops of the pendula are subjected to a sinusoidal horizontal driving force.

We need to add damping.

George - could that be solved without differential equations? I doubt it.

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. Now we have a real challenge.

[george7]

It's not doctoral stuff, but a reasonable model would be a high-end undergraduate problem. Consider thirty uniform physical pendula arranged in a line, each rigidly fixed at the top, linked with a horizontal low-constant spring to the next one midway up. The tops of the pendula are subjected to a sinusoidal horizontal driving force.

We need to add damping.

George - could that be solved without differential equations? I doubt it.

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. Now we have a real challenge.

I think you can explain most questions anecdotally, with a few equations here and there. I think you can come up with most of the elements of a kilt's swing without differential equations. If you treat the model as an accordion-like object that forms a semi circle, add in some friction at the pleat contacts... then you really only have to figure out the motion of a few of the pleats, the outer most pleats and a center pleat.

Your example sounds like a newton's cradle with some rubber bands. That still leaves out the whip effect some get with their end pleats... although that might explain a kilt that is out of phase with the wearer's pace.

For that... try swinging your single pendulum (a heavy rope with nothing on the end would be even better), then swing it back the other way just before it's ready to stop.

The kilt is a bit longer than most people's stride, so it is forced back slightly before it's natural rhythm.

Voila, a good Physics I explanation for the kilt whip.