Re: Eulerian angles
- To: mathgroup at smc.vnet.net
- Subject: [mg42677] Re: [mg42668] Eulerian angles
- From: "Dr. Robert Kragler" <kragler at fh-weingarten.de>
- Date: Sun, 20 Jul 2003 06:20:56 -0400 (EDT)
- Organization: Rechenzentrum
- Reply-to: kragler at fh-weingarten.de
- Sender: owner-wri-mathgroup at wolfram.com
Hallo Selwyn Hollis, my attention got caught by the subject "Euler angles" of your question. There is a nice chapter I found in the book of John W. Gray "Mastering Mathematica" Chapt. 6.2 which I tried to improve for my own lectures. You may download the Mathematica notebook "EulerAngles&3DRotations.nb" from my home page http://www.fh-weingarten.de/~kragler/public/ . I hope it answers your question. Another very good source is in the classics textbook by Herbert Goldstein "Classical Mechanics" Addison-Wesley Chapt. 4.4 (I hope the German edition from 1963 coincides with the original English version from 1959) and of course Eric Weisstein's "CRC Concise Encylopedia of Mathematics" (1998), ibidem p. 570 which is also found on WRI web pages in interactive form. What I was originally interested in is the inverse problem : given the position in Cartesian coordinates (on a sphere) and determine the corresponding Euler angles. As far as I understand it this problem has no straightforward solution only using nonlinear least square fitting. Perhaps, you are aware of a good treatment of this inverse problem. Greetings, Robert Kragler Date sent: Sat, 19 Jul 2003 03:20:01 -0400 (EDT) Subject: [mg42677] [mg42668] Eulerian angles From: Selwyn Hollis <selwynh at earthlink.net> To: mathgroup at smc.vnet.net > Some 5 or 6 years ago, I asked a question in MathGroup about the "Euler > angles" that are used by RotateShape. Apparently physicists know all > about this stuff, but I still have almost no feeling for what these > angles are about. So I thought I'd issue this challenge: > > Create *the* graphic illustrating the Euler angles that ought to be in > the Mathematica Book --- hopefully understandable by a hack > mathematician and his calculus students. > > The winner will receive glowing praise and thanks in a soon-to-be > published book. > > ----- > Selwyn Hollis > http://www.math.armstrong.edu/faculty/hollis > --------------------------------------------------------------------- Prof. Dr. Robert Kragler Fachhochschule Ravensburg-Weingarten/University of Applied Sciences Faculty Technology & Management Deputy Rector of Research & International Relations/Head of Computer Center P.O.B 1241, D-88241 Weingarten, Germany Tel: +49 751 501-9539 (Deputy Rector F) Tel: +49 751 501-9603 (Computer Center) Fax: +49 751 501-5-9603 E-Mail: kragler at rz.fh-weingarten.de HomePage: http://www.fh-weingarten.de/~kragler ---------------------------------------------------------------------