Re: Eulerian angles
- To: mathgroup at smc.vnet.net
- Subject: [mg42711] Re: Eulerian angles
- From: "John Doty" <jpd at space.mit.edu>
- Date: Tue, 22 Jul 2003 04:40:45 -0400 (EDT)
- Organization: MIT Center for Space Research
- References: <bfdqms$skt$1@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
In article <bfdqms$skt$1 at smc.vnet.net>, "Dr. Robert Kragler" <kragler at fh-weingarten.de> wrote: > 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. Well, you need at least two vectors in each frame. While the least-squares problem is nonlinear, if it is formulated carefully the nonlinearity is relatively benign and an iteritive method can converge very rapidly. I have a notebook describing this at: http://space.mit.edu/~jpd/LinTrigFunc.html This describes a way of obtaining the matrix representation of a rotation: once you have that, of course, it is straightforward to solve for your favorite Euler angles. -- John Doty "You can't confuse me, that's my job." Home: jpd at w-d.org Work: jpd at space.mit.edu