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Theory Manual Version 3.6
 Subsubsection 7.9.6.1: Prescribed Displacement at Joint Up Subsection 7.9.6: Prescribed Joint Motion Subsection 7.9.7: Other Rigid Connectors 

7.9.6.2 Prescribed Rotation at Joint

The relative rotation between the rigid bodies is We want it to be equal to a rotation by as expressed in the basis , We enforce this constraint by requiring that We may thus evaluate and expect that when the constraint is enforced. Note that because of the orthogonality of and , i.e., is always orthogonal, even when the constraint is not enforced. The axial vector of may be denoted by , i.e., , and the constraint is enforced when . Therefore, a moment needs to be prescribed,
Since is orthogonal, we can linearize it along an increment , , from which it follows that with so that From this expression we get Thus, It follows that and
 Subsubsection 7.9.6.1: Prescribed Displacement at Joint Up Subsection 7.9.6: Prescribed Joint Motion Subsection 7.9.7: Other Rigid Connectors