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If the analytic expression is known for equation (1),
then the evaluation of the Jacobian could be done by straightforward
differentiation.
For example, equation (6) for a structure with 6 DOF in 6D Cartesian space
(3D for position, 3D for rotation) - (*Figure 2b*) can
be expressed as:

If the analytic expression is unknown for equation (1),
numerical construction for the Jacobian is used. The Jacobian
is obtained column by column from the transformation matrices
[Chi96].

Lukas Barinka
2002-03-21