math - Python: Rotation Matrix to Angles -


given rotation matrix

     | r00  r01  r02 |  r = | r10  r11  r12 |      | r20  r21  r22 |

and specific rotation sequence 'abc' a, b, c taken 'xyz'. there general solution (for arbitrary rotation sequence) available in python translate rotation matrix rotation angles around x, y, , z axis?

it seems every rotation sequence has separate solution. given sequence "zyx" resulting symbolic expression rotation matrix is

       |      cy cz              -cy sz             sy  | rxyz = │  sx sy cz + cx sz   -sx sy sz + cx cz   -sx cy │        | -cx sy cz + sx sz    cx sy sz + sx cz    cx cy |

with c , s cosine , sine. x, y, z indices note rotation around x, y, , z axis. that, set of equations may derived, namely:

           cy cz = r00          - cy sz = r01          - sx cy = r02 sx sy cz + cx sz = r10       ...

those need resolved @ least 1 angle expression each axis. then, 'arcsin' or 'arccos' applied real angle. seems symbolic math needs performed each sequence separately.


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