# Quaternion Integration - And conversion to 3D matrix

I have a rotation matrix let us say $R(t)$ and its quaternion $q(t)$. We know already how to convert a quaternion to rotation matrix. Now if I want find $\int R(t) \ dt \tag1$ can we do that in quaternion domain somthing like $\int q(t) \ dt \tag 2$ and convert back to 3D matrix form. ? If not how?

• It is rather odd as to why you need to integrate rotation matrix. Its not a matrix algebra and integration is meaningless. – Troy Woo Oct 4 '14 at 12:57
• Come on.. I am currently working on such case..Rotation matrix represents orthogonal frames in curves and we can extract position vector by integration. – Nirvana Oct 4 '14 at 13:02
• I think the answer is negative. Rotation matrix and quaternion have rather different interpolation properties. – Troy Woo Oct 4 '14 at 13:04