Re: Euler rotation angles

*To*: mathgroup at smc.vnet.net*Subject*: [mg46748] Re: [mg46739] Euler rotation angles*From*: Oleksandr Pavlyk <pavlyk at phys.psu.edu>*Date*: Fri, 5 Mar 2004 01:46:58 -0500 (EST)*Organization*: Penn State University; Department of Physics*References*: <200403040547.AAA14288@smc.vnet.net>*Reply-to*: pavlyk at phys.psu.edu*Sender*: owner-wri-mathgroup at wolfram.com

Hi Sam, You should have been more specific about what dimensions your vectors are. I would assume they are 3-dimensional. Two vectors, call them v1, v2, span a plane. Two vectors can be rotated into one another only if they have the same length. So I will assume they do. Within that plane, the angle between them can be found phi = ArcCos[ (v1.v2)/Sqrt[ (v1.v1) (v2.v2) ] ] The perpendicular vector to that plane can be found using cross product perp = Cross[ v1, v2 ] Is this vector vanishes, then your vectors are parallel. The the sought after rotation is around vector perp through the angle phi found above. Let us define {nx, ny, nz} = perp/ Sqrt[ perp.perp ] ; The matrix rot, that implements this rotation in 3 dimensions looks as this rot = MatrixExp[ phi { { 0, nz, -ny}, { -nz, 0, nx}, {ny, -nx, 0} } ] rot.v2 == v1 gives True. To understand the group of rotations in 3 dimensions better you could consult some of books on the subject, like "Representations of the rotation and Lorentz groups : an introduction" by Moshe Carmeli available at Amazon (used). see also http://mathworld.wolfram.com/Rotation.html Best, Sasha S. Campbell wrote: > Hi, > > Can anyone help me with the following? I have two vectors, one rotated > with respect to the other, and I wish to find the Euler rotation > angles that connect the vectors. Can mathematica tell me what the > required angles are? > > Cheers, > > Sam

**References**:**Euler rotation angles***From:*sam_campbell@hotmail.com (S. Campbell)