A perturbation analysis for the dynamical simulation of mechanical multibody systems

The dynamical behaviour of mechanical multibody systems with holonomic constraints is described by the Euler{Lagrange equations. In the present paper various approaches to the numerical integration of this diierential-algebraic system are compared w. r. t. the sensitivity of the numerical solution to small errors (e. g. round-oo errors that arise in the implementation on a computer). Position and velocity coordinates are proved to be much more robust against small perturbations than the Lagrangian multipliers. A comparison of systems with and without friction shows that small errors are substantially more ampliied during integration if friction occurs.