The equations of motion of a mechanical system can be written in the form of a system of differential algebraic equations (or "DAEs") of indez 3. A simulation of the movements of such systems requires reliable and efficient numerical methods. However, the higher the index of a system of DAEs, the more difficult its numerical treatment, we thus choose to consider the mechanical equations brought into an index 2 formulation by differentiating

once the algebraic constraints.

A new class of numerical methods, the half-explicit methods, for solving index 2 semiexplicit DAEs is presented. These methods are defined, their convergence is studied, then the order conditions are derived with the help of symbolic structures - the trees - and methods up to order 5 are constructed.

With the aim to give these results available for researchers and ingeneers confronted to realistic and practical applications, we have carefully implemented a half-explicit method of order 5 in a FORTRAN code called HEMS. This code is directly written to solve the mechanical equations in the index 2 formulation. Furthermore, it offers a lot of options, among them, a projection to satisfy the original constraint of index 3, two dense output

formulas, the choice of linear algebra routines, such as the UMFPACK routines for solving sparse sytems.

Finally, the code HEMS is tested on an amount of interesting problems, and comparisons with some other codes point out its very good performances.