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18.104.22.168 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 22.214.171.124↑. 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 (126.96.36.199-7). Similarly, where Combining these results produces