Re: Cylindrical to helix transformation
- To: mathgroup at smc.vnet.net
- Subject: [mg27890] Re: Cylindrical to helix transformation
- From: Erk Jensen <Erk.Jensen at cern.ch>
- Date: Fri, 23 Mar 2001 04:31:09 -0500 (EST)
- References: <99ci74$8gv@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
Andy Qualls wrote:
>
> Greetings --
>
> We have a length of tubing with a line drawn down its length. The line is
> marked off in inches. We want to know how how that line would transform when
> we shape the tube into a helix.
>
> I looked through my math books and could not find the cylindrical to helical
> transformation.
>
> How would I do such a transformation in Mathematica?
>
> TIA
>
> Andy Qualls
You want to bend the tube, did I get you right? Then you want to know what
length of tube you would need to make a certain given helix?
Well - if the tube is thin compared to the bending radius, you can take the
length of a helical line which is easy. Imagine all the helix is sitting on the
surface of a circular cylinder of radius "r", and after one winding you are by
"a" further down the axis. The length of such a "winding" is l = Sqrt[a^2 + (2
Pi r)^2]
So, "r" and "a" define the pitch angle of your helix.
If your helix has x windings, then the length of the cylinder is x*a, the length
of the shaped tube is x*l. Of course, x is not necessarily integer ...
If the tube is not "thin", your question is more mechanical than mathematical.
Does this answer your question (maybe I didn't get it)?
Ciao
-erk-