Stable Underlying Equations for Constrained Hamil- tonian Systems

Constrained Hamiltonian systems represent a special class of differential algebraic equations appearing in many mechanical problems. We survey some possibilities for exploiting their rich geometric structures in the numerical integration of the systems. Our main theme is the construction of underlying equations for which the constraint manifold possesses good stability properties. As an application we compare position and momentum projections for systems with externally imposed holonomic constraints.