- View Source
On Jul 31, 2006, at 7:10 PM, C Goodman-Strauss wrote:

Hello, in the Advanced Applied class I'm teaching (aka A First Look at

Fourier Series Stuff), we are going over solving various physically

motivated boundary value problems. A problem came up today, describing

the motion of a rod fixed at one end, given a vigorous twist and

released. The solution seemed a little weird looking, so I made a GC

file to take a look. I dunno, does this look realistic?

Have fun,

Chaim

----------

No!

At first glance it didn't seem right

Then looking closer I expected the twist to start at the moving end and

travel downward to the fixed end

So I would say it looks OK with n

going 0 to 1, 2 to 3, 4 to 3, and 2 to 1

But to me it doesn't look right with n

going 1 to 2, 3 to 4, 3 to 2, and 1 to 0

a good distraction to my busy day

Arne - View SourceOn Jul 31, 2006, at 10:10 PM, C Goodman-Strauss wrote:

>

> Hello, in the Advanced Applied class I'm teaching (aka A First Look at

> Fourier Series Stuff), we are going over solving various physically

> motivated boundary value problems. A problem came up today, describing

> the motion of a rod fixed at one end, given a vigorous twist and

> released. The solution seemed a little weird looking, so I made a GC

> file to take a look. I dunno, does this look realistic? - View SourceHere's a fun variation on the twisty rod file: Simply plot z=A(x,y);

this shows, at x,y, the amount twisted at position x along the rod, at

time y. However, really, for the rod, 0<x<1 and y>0 (shown in red). If

we look at a larger domain, we see that the series sums up to an

egg-carton shape, with square pyramids, up and down, for the dimples.

(Alternatively, this could be seen as the top of a layer of packed

rhombic dodecahedra)

As far as I can tell, the edges are actually sharp, at least as the

number N of terms increases. (Even around n=10 or so, they would appear

perfectly sharp, I think, if rendered exactly, but GC is assembling the

picture out of little squares)