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