Theory Manual Version 3.4
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Subsubsection 7.9.4.2: Reaction Moments from Torsional Springs Up Subsection 7.9.4: Joint Reaction Forces and Moments Subsubsection 7.9.4.4: Reaction Moments from Torsional Dampers

#### 7.9.4.3 Reaction Forces from Dampers

The reaction force on a damper is where is the time rate of change of the gap function, and represents a projection as described in Section 7.9.4.1↑. In particular, is used with spherical and revolute joints; is used with prismatic and cylindrical joints; and is used with planar joints. The parameter represents the damping coefficient.
The velocities of the insertion points are given by , where is the rigid body angular velocity. The linearization of is where with Recall that and are the Newmark parameters, and is given in (6.3.4.1-7). Similarly, where Combining these results produces
Subsubsection 7.9.4.2: Reaction Moments from Torsional Springs Up Subsection 7.9.4: Joint Reaction Forces and Moments Subsubsection 7.9.4.4: Reaction Moments from Torsional Dampers