Re: Questions regarding quaternions
- From: Zerex71 <Zerex71@xxxxxxx>
- Date: 3 May 2007 07:08:38 -0700
On Mar 6, 2:56 pm, "Zerex71" <Zere...@xxxxxxx> wrote:
On Mar 1, 11:02 am, "G. A. Edgar" <e...@xxxxxxxxxxxxxxxxxxxxxxxxxxx>
wrote:
a. Take an object (e.g. vector) and rotate it in space to a new
desired orientation
b. Take a frame of reference (or measurements therein) and convert it
to another frame of reference (or measurements referenced that second
frame) without rotating it
Some classic textbook (maybe Birkhoff & MacLane) call these
"alias" and "alibi".
--
G. A. Edgar http://www.math.ohio-state.edu/~edgar/
I found this which, read as written, makes perfect sense to me!http://mathworld.wolfram.com/AlibiTransformation.htmlhttp://mathworld.wolfram.com/AliasTransformation.html
Cheers,
Mike
I'm back!
I am actually developing something for work which requires the use of
both alibi and alias transformations, but I have run into a bit of a
snag.
I will reference these articles and their conventions on rotations:
http://mathworld.wolfram.com/RotationMatrix.html
http://mathworld.wolfram.com/EulerAngles.html
I am trying to compute the point in space where the muzzle of a
vehicle main gun is pointing if the turret rotates in azimuth and
elevation.
The problem is, when determining the DCM (A, which = BCD), I get some
minor sign errors. I believe these result from me not being able
to figure out which sin's and cos's I should be putting the negatives
on, according to these articles. I am trying to do the rotation where
the object (point) moves, not the coordinate system, and while I
managed to get the numbers I was looking for, I had to do a bit of
temporary
sign-futzing to make it work. I am confused as to why, according to
the articles, you use a different set of signs (looks like a transpose
of
sin theta's to me) for each type of rotation. If that's the case, so
be it, I was just under the assumption one set of matrix
multiplications would
suffice for both types of tranformation (alias and alibi). I want to
understand *exactly* what B, C, and D I should be using.
The specific problem is this: On a vehicle, I have two coordinate
systems, one for the hull (point O_H), which is located at the ground
plane, left front track,
and one for the turret (point O_T), about which the turret rotates.
For the sake of convenience, both coordinate systems are parallel
(i.e. no angular offset
set in any of the three axes). I know the point in space where the
muzzle of the gun is by default in both systems. Now I rotate the gun
a specified
(az,el) (yaw, pitch, roll=0) and want to calculate the new point in
space, relative to the hull origin, where the muzzle is. This is my
method:
1. Starting with the muzzle relative to the turret r1 = (x,y,z),
rotate by the specified amount (az,el).
2. Create the DCM A = BCD from the individual rotations.
3. Create r2 = A*r1 (vector multiplied by a matrix), giving the new
(x,y,z) relative to the turret.
4. Add r0 (vector from O_H to default muzzle position) to the vector
difference between r2 and r1 (r2-r1) to yield r_rot, the new point in
space relative to the hull origin.
Comments are welcome!
.
- Prev by Date: Re: Cantor Confusion
- Next by Date: Re: Reverse factor date
- Previous by thread: Reverse factor date
- Next by thread: Probably haven't seen this one, but...
- Index(es):
Relevant Pages
|
