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Tue, 31 Jan 2017 18:24:07 -0800

Could you show what you are doing to get the statement "However, I cannot
reproduce this matrix via composition; i.e. by multiplying the underlying
rotation matrices.". I would guess something involving the `*` operator
instead of `@`, but guessing probably won't help you solve your issue.

    -Joe



On Tue, Jan 31, 2017 at 7:56 PM, Seb <splu...@gmail.com> wrote:

> Hello,
>
> I'm trying to compose Euler rotation matrices shown in
> https://en.wikipedia.org/wiki/Euler_angles#Rotation_matrix.  For
> example, The Z1Y2X3 Tait-Bryan rotation shown in the table can be
> represented in Numpy using the function:
>
> def z1y2x3(alpha, beta, gamma):
>     """Rotation matrix given Euler angles"""
>     return np.array([[np.cos(alpha) * np.cos(beta),
>                       np.cos(alpha) * np.sin(beta) * np.sin(gamma) -
>                       np.cos(gamma) * np.sin(alpha),
>                       np.sin(alpha) * np.sin(gamma) +
>                       np.cos(alpha) * np.cos(gamma) * np.sin(beta)],
>                      [np.cos(beta) * np.sin(alpha),
>                       np.cos(alpha) * np.cos(gamma) +
>                       np.sin(alpha) * np.sin(beta) * np.sin(gamma),
>                       np.cos(gamma) * np.sin(alpha) * np.sin(beta) -
>                       np.cos(alpha) * np.sin(gamma)],
>                      [-np.sin(beta), np.cos(beta) * np.sin(gamma),
>                       np.cos(beta) * np.cos(gamma)]])
>
> which given alpha, beta, gamma as:
>
> angles = np.radians(np.array([30, 20, 10]))
>
> returns the following matrix:
>
> In [31]: z1y2x3(angles[0], angles[1], angles[2])
> Out[31]:
>
> array([[ 0.81379768, -0.44096961,  0.37852231],
>        [ 0.46984631,  0.88256412,  0.01802831],
>        [-0.34202014,  0.16317591,  0.92541658]])
>
> If I understand correctly, one should be able to compose this matrix by
> multiplying the rotation matrices that it is made of.  However, I cannot
> reproduce this matrix via composition; i.e. by multiplying the
> underlying rotation matrices.  Any tips would be appreciated.
>
> --
> Seb
>
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