Preprint des Projektes: Forschungsschwerpunkt Mathematisierung

Numerische Analyse Strukturbildender Prozesse

00-02 Christian Alscher.
Numerical simulation of impact and lift-off events in the hydrostatic skeleton of the leech

Abstract In this paper we present a mechanical model of the hydrostatic skeleton and simulate the collision with an obstacle. The model is based on the worm-like shape of the medicinal leech and consists of a sequence of hexahedral segments with elastic edges and constant internal volume. Lagrange's equations of motion with holonomic constraints for the volume lead to a differential-algebraic system (DAE). The contact of the model with an obstacle including tangential friction is realized by Coulomb's law, this leads to unilateral constraints in the system. A switching algorithm is set up to detect impact and lift-off events as well as sliding/sticking transitions during contact. In periods of smooth motion the DAE system is solved by semi-explicit numerical methods implemented in the code MEXAX.