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.
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preprint_63_98.ps (12MB (!), includes 7 illustrations)