Modeling and velocity stabilization of constrained mechanical systems
The use of some one- and multistep methods for the numerical integration of constrained mechanical systems with and without stabilization is discussed in order to compare their efficiency. In particular, the use of (high-order) multistep methods is considered. A descriptor form of the differential algebraic equation (DAE) formulation is used and applied to two non-stiff test problems. By index reduction, the DAE model is transferred to an equivalent ordinary differential equation (ODE) representation whose unstable numerical solution is stabilized by projection back onto the constraint manifold. A perturbation analysis shows that velocity stabilization is the most efficient projection with regard to improvement of the numerical integration. How frequently the numerical solution of the transferred ODE should be stabilized is discussed. For a class of multistep methods, a strategy of stabilizing at certain time steps and performing a much less demanding quasi-stabilization at the others is suggested, especially for high-order methods. With these high-order methods, stabilization is not even necessary for the second test problem.
scientific article; zbMATH DE number 739433
scientific article