Euler angles from Orientation Matrix
{"Image DocumentName": "Euler angles from Orientation Matrix", "Image ImageDescription": "Notes: the range of inverse cosine (ACOS) is 0-\u03c0, which is sufficient for \uf046; from this, sin(\uf046) can be obtained. The range of inverse tangent is 0-2\u03c0, so numerically one must use the ATAN2(y,x) function) to calculate \uf0661 and \uf0662. Caution: in Excel, one has ATAN2(x,y), which is the reverse order of arguments compared to the usual ATAN2(y,x) in Fortran, C (use \u2018double atan2 ( double y, double x ); \u2018) etc.! Also, if the second Euler angle is too close to zero, then the standard formulae fail because sine(\uf046) approaches zero (see next slide). The second formula deals with this special case, where the 1st and 3rd angles are linearly dependent; distributing the rotation between them is arbitrary. Corrected -a32 in formula for \uf0661 18th Feb. 05; corrected a33=1 case 13th Jan08.", "Image XResolution": "37", "Image YResolution": "37", "Image ResolutionUnit": "Pixels/Centimeter", "Image Software": "SlidePlayer", "Image YCbCrPositioning": "Centered"}