TABLE OF CONTENTS Let us recall that the dynamic part of the weak form of balance equations at time t n +1 is
| (110) |  |
where the test function ? t has to satisfy the algorithmic form of equation (23)
| (111) |  |
By exploiting analogy with equations (50) and (51) we may write ? t in terms of the incremental rotation vectors (introduced in Section 4 and used for the time discretization in Section 5) as
| (112) |  |
where 
and 
defined in equations (52) and (53), are now functions of the incremental rotation vectors 
and ? n +1, respectively. Equation (112) satisfy condition (111).
Linearization of ? t with respect to intrinsic rotational variables at time t n + 1, which are and ? n +1, is not zero. It can be shown that the following forms can be obtained from equation (112)
| (113) |  |
where 
and 
and 
are again functions of and ? n +1, respectively. Full form of 
is
| (114) |  |
where 
= and matrices A, B are defined as
| (115) |  |
Full form 
of is given in an analogous way. Some further details may be found in Brank et al. (1997).
Finally, we note that the linearization of the shell-director at time t n + 1, namely ? t n
