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On the wikipedia page there is a listing of 12 matrices that can be used to represent a yaw-pitch-roll rotation series (YXZ) as a ZXZ rotation, or an XZX rotation, or an XZY rotation..

1) Should the ZXZ rotation matrix be exactly equal to the YXZ rotation matrix?

2) How are the ZXZ etc rotation matrices derived? How would you go about deriving a zxzxz rotation matrix?

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    I might have left it if it were `xyzzy`, though.2011-10-07

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(1) No -- the point (one of the points) is that they give different results. Therefore simply giving three angles is not sufficient to specify a rotation in space; one must also have agreed which of the 12 conventions one is using. (Each of the conventions can specify all rotation matrices, but they do it with different angle triples).

(2) The display above the table of 12 matrices show the rotation matrices $\mathrm{Rot}(Y,\theta)$, $\mathrm{Rot}(X,\theta)$, and $\mathrm{Rot}(Z,\theta)$. Each entry in the table is then just the worked-out product of the three matrices specified -- for example, ZXZ is the matrix product $\mathrm{Rot}(Z,\theta_1)\mathrm{Rot}(X,\theta_2)\mathrm{Rot}(Z,\theta_3)$.

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    Yes, you can, check out [here](http://en.wikipedia.org/wiki/Rotation_representation_(mathematics)#Conversion_formulae_between_representations)2011-10-08