This project features a "SpineBushing" element that can be used to model the intervertebral disc as a 6x6 stiffness matrix. This permits the study of the disc's force-motion relationship for the case where the coordinates are coupled to each other.

The guiding equation is,

F_2 = -K * Delta_Q

where F_2 is the generalized 6x1 force vector acting on the upper vertebra, K is a stiffness matrix, and Delta_Q is the generalized 6x1 displacement vector specifying the change in position from neutral between the points of attachment of the stiffness element.

By Newton's 3rd law,

F_1 = - F_2.

The SpineBushing features two *key* differences from the existing bushing element:
(1) we incorporated a full 6x6 stiffness matrix instead of the current three translational and three rotational stiffnesses.

(2) the **change** in relative motion is used and not the relative motion itself. In 1-D, you can think of this as having a spring with a resting length equal to the distance between the specified attachment points on the two bodies in the neutral posture. (The typical bushing element, on the other hand would be analogous to a spring with zero resting length.)

Further details are provided in the accompanying documents.