TABLE OF CONTENTS It has been noted (Betsch et al., 1998) and (Ibrahimbegovi? et al., 2001) that an attractive parametrization of constrained finite rotation with the total rotation vector ( 
or ? ) will exhibit the singularity problem whenever its norm reaches a multiple of ?. For overcoming this deficiency we introduce in this section an incremental rotation vector which, moreover, is fully consistent with the standard incremental solution scheme for nonlinear problems. Since it maintains additive iterative rotational updates it is also very suitable for optimization problems (Kegl, 2000; Ibrahimbegovi? and Knopf-Lenoir, 2001).
The evolution of configuration space variables is obtained by a step-by-step integration scheme. The time interval of interest is partitioned into the number of time steps: 0 < t 1 < t n < t n + 1 < < T. At the typical time, t n, the values of translational and rotational motion components are denoted as
| (73) |  |
where t n is defined via orthogonal tensor ? n = ?( t n) through relation t n = ? n e.
Let us now substitute total rotation vectors (material version) and ? (spatial version) by the corresponding incremental rotation vectors n +1 and ? n + 1, which are reset to zero at the beginning of each solution increment. Without going through a...
