Re: [Algorithms] Rotation Matrices

[<dav...@hu...>]

    Imagine rotating a cylinder in 3 dimensions about the 2 of the 3
principle axis.  This works best if you pick up a cylindrical medicine
bottle or something similiar (it helps to visualize).  Let's assume y is up,
x is left to right and z is towards and away from you.    Hold the cylinder
such that the "length" of the object points in the direction of y axis and
the "flat" section parallels the x axis.   Now perform these rotations:

a)
      - rotate 45 degrees around the y axis.  (you should notice the
cylinder just spins "in place", and does perceptually move if its a perfect
cylinder).
      - rotate 45 degrees about the x axis.  (it now leans toward or away
from you depending on the direction of rotation).

b)
      - rotate 45 degrees about the x axis. (it now leans toward or away
from you depending on the direction of rotation).
      - rotate 45 degrees around the y axis.  ( the cylinder now is at an
angle in more than one axis.)


As you can hopefully see, the order of rotations in 3 dimensions makes a
difference.


----- Original Message -----
From: <Nik...@ao...>
To: <gda...@li...>
Sent: Wednesday, August 02, 2000 1:25 PM
Subject: [Algorithms] Rotation Matrices


> Why isn't the multiplication of rotational matrices commutative?  For
example
> if I have one rotation matrix which rotates 20 degrees around the Z axis,
and
> another which rotates 50 degrees around the X axis, depending on the order
in
> which I multiply them, I get different results.  Why is this?  When
rotating
> an object there is no visible difference when it is first rotated on one
axis
> and then on another, is there?  I first looked in an elementary linear
> algebra book for the answer; however it stated that the multiplication of
> rotation matrices is commutative (although it was only covering 2D
rotation
> matrices). Any help would be appreciated.
>
> Thanks,
> Nik...@ao...
>
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