🚀 go-pugleaf

Remco de Korte wrote:

> Here's a second try and my idea of a way to find a solution:
> two points can move relative to eachother, as if they're connected with
> a tube. This tube won't stretch, but it may bend, while it's length is
> constant. I want to know a way to describe the curve of this tube.

It appears to me that this is more a physics problem than a geometric
one.In order to obtain a unique shape as the end points of an elastic rod
move
relative to each other, you must describe its mechanical properties, such
as stiffness, torsion, tension, potential energy etc. Mathematically
speaking,
I don't see how your conditions would lead to a unique solution. If it's
just a
one-dimensional problem, you may get away with solving a boundary
value problem in form of a second order ordinary differential equation,
so your best bet would be a book on Solid Mechanics, Elasticity, Mechanical

Engineering or the like. "Finite Difference Methods" come to mind...

> The way I see it is that if you know the length of the 'tube' (which you
> may assume) and the coordinates of the points (which are variable) you
> must find a circle throught the two points where the part of the circle
> between thos points is equal to the length of the tube. Problem is, I
> even forgot how to calculate the length of a circle-segment....

Once you've decided on the radius of the circular arc joining the two
points,
you cannot move them relative to each other and independently any more.
If you change the radius, you change the arclength, which is not permitted
according to you. I'm afraid circles won't do...

I hope this helps,
Matthias Weiss
mmshiro@math.lsa.umich.edu