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MathGroup Archive 2001

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Re: Rotation3D, MatrixRotation3D ?

  • To: mathgroup at smc.vnet.net
  • Subject: [mg30409] Re: Rotation3D, MatrixRotation3D ?
  • From: "ojg" <ole.jonny.gjoen at hitecvision.com>
  • Date: Fri, 17 Aug 2001 03:09:49 -0400 (EDT)
  • References: <9lalnl$cd3$1@smc.vnet.net> <9ld1o3$2gl$1@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

The three rotational axes (X,Y,Z) stays fixed and orthogonal in original
space. All angles are relative these.

I guess you can let these axes define a coordinate system XYZ in original
space, which is beeing rotated through the fixed original axes (rot axes do
not follow the rotations). Given that the resulting rotated system will have
axes of x, y,z what are the angles of rotations?

I have given a simplified problem, but given the solution to this any other
general problem I have may be solved.


"Kevin J. McCann" <kevinmccann at Home.com> wrote in message
news:9ld1o3$2gl$1 at smc.vnet.net...
> I believe the documentation for RotationMatrix3D says it all.
>     1) Rotate by phi about z-axis
>     2) Rotate by theta about the new x-axis
>     3) Rotate by psi about the even newer z-axis
> This is a rotation of the coordinate system, NOT the vector. To rotate the
> vector instead you must reverse the order and signs of the angles. As far
as
> your problem goes, I am not sure about the statement. Are the three angles
> the angles from the 3 axes of your new vector or ...?
>
> Kevin
>
> "ojg" <ole.jonny.gjoen at hitecvision.com> wrote in message
> news:9lalnl$cd3$1 at smc.vnet.net...
> > Question regarding rotations.
> >
> > Some of the documentation found regarding this is not as far as I can
see
> > complete in the documentation, at least the subject is difficult enough
to
> > make me unsure once not 100% clear:)
> >
> > Fist, what are the defined "euler angles" in mathematica, and in what
> order
> > are they applied?
> >
> > Second, of which side of the vector is the rotational matrix multiplied
?
> >
> > Third, is there a mathematica way to rotate around an abitrary
rotational
> > axis? If not, what would the mathematica matix be for this?
> >
> > My problem to solve is as follows: Given three rotational angles (a,b,c)
> > applied in order to the following three rotational axes: Y axis, X axis,
Z
> > axis. (usual right hand system). This rotation applied to any vector v
> will
> > give you a vector V (first Y rotation applied on v, etc).
> >
> >
> > Now, given a rotational matrix with pure numerical values in, I need to
> find
> > the three angles, and I need a general formulae for this solution taking
> > care of the special cases.
> >
> > Thanks,
> > Johnny
> >
> >
> >
>
>


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