Conservation properties of a time FE method - part III: Mechanical systems with holonomic constraints

A Galerkin-based discretization method for index 3 di:erential algebraic equations pertaining to >nitedimensional mechanical systems with holonomic constraints is proposed. In particular, the mixed Galerkin (mG) method is introduced which leads in a natural way to time stepping schemes that inherit major conservation properties of the underlying constrained Hamiltonian system, namely total energy and angular momentum. In addition to that, the constraints on the con>guration level and on the velocity=momentum level are ful>lled exactly. The application of the mG method to speci>c mechanical systems such as the pendulum, rigid body dynamics and the coupled motion of rigid and Aexible bodies is presented. Related numerical examples are investigated to evaluate the numerical performance of the mG(1) and mG(2) method