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angular velocity representation

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It seems that the common way to describe angular velocity in 3D is with a 3D vector, the vector''s direction is parallel to the axis of rotation and its magnitude is the size of the angular velocity. (I suppose it is like Axis Angle representation) However I unknowingly used what I thought was the Euler''s angle representation in my program, that is a 3D vector where each element represent the signed speed of rotation about one of the 3 main axes. It seems to work with all equations, but it is probably wrong somewhere. Are the two essentially the same? If not, how do you get from Euler angles to the common representation.

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