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MathGroup Archive 2001

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Re: Rotation3D, MatrixRotation3D ?

  • To: mathgroup at smc.vnet.net
  • Subject: [mg30429] Re: Rotation3D, MatrixRotation3D ?
  • From: "Kevin J. McCann" <kevinmccann at Home.com>
  • Date: Sat, 18 Aug 2001 04:04:55 -0400 (EDT)
  • References: <9ld1m6$2gi$1@smc.vnet.net> <9lig7d$iqc$1@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

I am not sure what you mean; so, let me restate it a little. To use your
notation, there is an XYZ coordinate system that is fixed in the LAB, often
called the LAB system. This system is fixed for all time. If we now think of
a second system xyz that originally lines up with XYZ, then we do the
following:
    1) rotate the xyz system by phi about the Z-z axis
        we now have a new x'y'z' system in which z'=z=Z axis
    2) rotate x'y'z' through theta about the x' axis
        we now have an x''y''z'' system in which x''=x' axis
    3) finally, rotate x''y''z'' throug psi about the z'' axis to
        get the final orientation of the new coordinate system

The rotations as applied rotate the coordinate system relative to the LAB
system. You can see this by seeing what happens with

    RotationMatrix3D[phi,0,0].{1,0,0}
    RotationMatrix3D[phi,0,0].{0,1,0}
    RotationMatrix3D[phi,0,0].{0,0,1}

What you will see is that the three unit vectors are NOT rotated through phi
(positive is by the right-hand-rule, by the way), but appear to be rotated
through -phi, i.e. as viewed from the new system.

Kevin



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