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Theory Manual Version 3.6
 Subsubsection 6.3.1.2: Cayley Transform Up Subsection 6.3.1: Rigid Body Rotation Subsection 6.3.2: General Rigid Body Motion 

6.3.1.3 Linearization Along Rotational Increment

Let represent a spatial rotational increment, such that a rotation tensor compounded by an infinitesimal incremental rotation is given by Using the Cayley transform for illustration, the linearization of along the increment is obtained from The same result may be obtained with the exponential map. Similarly, using an infinitesimal material rotational increment such that , we may find
 Subsubsection 6.3.1.2: Cayley Transform Up Subsection 6.3.1: Rigid Body Rotation Subsection 6.3.2: General Rigid Body Motion