Re: Spirals and arc length
- To: mathgroup at smc.vnet.net
- Subject: [mg41278] Re: Spirals and arc length
- From: Jens-Peer Kuska <kuska at informatik.uni-leipzig.de>
- Date: Mon, 12 May 2003 04:36:09 -0400 (EDT)
- Organization: Universitaet Leipzig
- References: <b9n9ki$8sl$1@smc.vnet.net>
- Reply-to: kuska at informatik.uni-leipzig.de
- Sender: owner-wri-mathgroup at wolfram.com
Hi, http://mathworld.wolfram.com/LogarithmicSpiral.html may help you. Regards Jens DIAMOND Mark wrote: > > 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