Services & ResourcesWolfram ForumsMathGroup Archive

[Date Index] [Thread Index] [Author Index]

Spirals and arc length

• To: mathgroup at smc.vnet.net
• Subject: [mg41271] Spirals and arc length
• From: "DIAMOND Mark" <noname at noname.com>
• Date: Mon, 12 May 2003 00:58:33 -0400 (EDT)
• Organization: The University of Western Australia
• Sender: owner-wri-mathgroup at wolfram.com

Please excuse the double posting, but I am interested in both the
mathematics and a Mathematica approach to the following problem.

Simply put, I wish to find the polar coordinates of a point that has been
moved along a spiral arc.
If I have a point (theta0,r0) on a spiral r=a Exp(b*theta), and I travel
along the spiral arc some distance (delta), then what are the polar
coordinates of the new point?

I would really like a few different things if anyone can help; not
necessarily in priority order ...
(1) a simple expression for the answer;
(2) an explanation that I can follow and apply to a spiral of a different
form, say Archimaedian or hyperbolic;
(3) a Mathematica approach to *deriving* the appropriate expression.

This may be too much to ask, but I have tried tackling the problem myself
and even having read the mathworld entries on the various spirals (and
arc-length), I'm not sure where to begin.

Cheers,

--
Mark R Diamond
Vision Research Laboratory
The University of Western Australia
email: FirstNameFollowedbySurnameInitialAtpsy.edu.au

• Follow-Ups:
  • Re: Spirals and arc length
    • From: David Terr <dterr@wolfram.com>