Preprint des Projektes: DFG Schwerpunkt Programm: Ergodentheorie, Analysis und effiziente Simulation dynamischer Systeme

Verbindungsorbits in hochdimensionalen dynamischen Systemen

63/98 Christian Alscher, Wolf-Jürgen Beyn.
Simulating the motion of the leech: A biomechanical application of DAEs

In this paper a mathematical model is developed for the dynamical behaviour of a hydrostatic skeleton. The basic configuration is taken from the worm--like shape of the medicinal leech. It consists of a sequence of hexahedra with damped elastic springs as edges to model the various parts of the musculature. The system is stabilized by the constraint of constant volume either in the whole body or in prescribed compartments. We set up Lagrange's equations of motion with the Lagrange multipliers being the pressure values in the compartments. The equations of motion lead to a large differential--algebraic system which is solved by an application of semi--explicit numerical methods. Though the model has not yet been adapted to experimental data, first simulations with a simplified set of parameters show that it is capable of generating basic movements of the leech such as crawling and swimming.