**Edit 19 Sept 2010. I strongly recommend using the eigenvector rather than trying to make a unit vector out of the off-diagonal terms. Find “edit” below.**

Back in what has turned out to be my most popular post, axis and angle of rotation, I showed how to switch between the angle and axis of rotation and the rotation matrix.

Given the axis of rotation as a unit vector (a, b, c), and the angle of rotation, we construct the matrix N

and then we construct

and that’s a rotation. To be specific, it is an attitude matrix for a rotation of coordinate axes, about the axis (a, b, c) through the angle .

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