Preprint des Projektes: DFG Schwerpunkt Programm: Ergodentheorie, Analysis und effiziente Simulation dynamischer SystemeVerbindungsorbits in hochdimensionalen dynamischen Systemen63/98 Christian Alscher, WolfJürgen Beyn. In this paper a mathematical model is developed for the dynamical behaviour of a hydrostatic skeleton. The basic configuration is taken from the wormlike 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 differentialalgebraic system which is solved by an application of semiexplicit 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.
