Preprint des Projektes: Forschungsschwerpunkt Mathematisierung

Numerische Analyse Strukturbildender Prozesse

00-01 Christian Alscher.
Sensitivity analysis of impact and lift-off events in constrained mechanical systems

We consider mechanical systems with holonomic constraints given by equalities and unilateral constraints that arise in contact problems. Impact or lift-off events lead to jump discontinuities in the velocities and delta-functions in the Lagrange multipliers, and we find piecewise smooth solutions of the equations of motion. In the special case of one isolated event we study the sensitivity of the solution w.r.t. small perturbations in the equations and in the constraints. We derive error bounds for the position and velocity coordinates and illustrate the results by a numerical example: the collision of a hydrostatic skeleton with an obstacle.