Re: Exponential Function for Quaternions ?
- From: pa@xxxxxxxxxxxxxxxxxxxxx (Pierre Asselin)
- Date: Tue, 2 Oct 2007 00:24:14 +0000 (UTC)
Peter Christensen <pc@xxxxxxxxxxxxxxxxxxx> wrote:
(What is a 'quat': http://en.wikipedia.org/wiki/Quaternions)
Does it make sence, simply to define it from Taylor series? -At least
that's what I'm trying. This definition should define a 'Quaternion
Exponential Function' (QEF) in a precise and welldefined way!
Yes.
If for example z = z_1 + j z_j + k z_k + l z_l = exp (theta) =
exp(theta_1 + j theta_j + k theta_k + l theta_l). Would it be possible
also to use exp(theta) = exp(theta_1)*exp(j theta_j)*exp(k
theta_k)*exp(l theta_l)?
Nope. Just exp(theta_1)*exp(i theta_i + j theta_j + k theta_k).
Quaternions don't commute so in general exp(a+b) != exp(a)exp(b).
I would also like to define a logarithm function for 'quats'. It won't
be a problem simply to let it be the inverse of the exponential
function: theta = ln(z). But if a and b are quats in general, then
will ln(a*b) = ln(a)+ln(b)?
No, for the same reason.
Are there someone else who are doing research in such representations
of rotations for quats, or eventually, does there already exist a
theory for these rotations. (I just thought, tht maybe I could have
been missing it, if it just use another representation/notation...)
Yes, but it's a long story. Try following the link
"Quaternions and spatial rotation" at the bottom of the Wikipedia
article.
The Wikipedia articles seem a little green. You may be
better served by a book from a mathematical library.
--
pa at panix dot com
.
- Follow-Ups:
- Re: Exponential Function for Quaternions ?
- From: Michael Murray
- Re: Exponential Function for Quaternions ?
- References:
- Exponential Function for Quaternions ?
- From: Peter Christensen
- Exponential Function for Quaternions ?
- Prev by Date: Re: A complex transcendental equation
- Next by Date: Re: A More Consistent Definition of Tetration for Rational Exponents
- Previous by thread: Exponential Function for Quaternions ?
- Next by thread: Re: Exponential Function for Quaternions ?
- Index(es):
Relevant Pages
|
|
