A perturbation analysis for the dynamical simulation of mechanical multibody systems

摘要

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 differential-algebraic system are compared with respect to the sensitivity of the numerical solution to small errors (e.g. round-off 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 amplified during integration if friction occurs.