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.
